The Doctor (title)

Although the wider universe usually considered the title of "the Doctor" to simply be the name of the Renegade Time Lord usually known as such, they actually viewed the identity of "the Doctor" as a persona they put on for the sake of the universe, embodying a promise they had made. (PROSE: The Day of the Doctor, TV: The Name of the Doctor) Hence, other individuals "became" the Doctor, being acknowledged by the original as equally valid claimants to the tile as themselves. (TV: Flatline, The Next Doctor) As one Doctor put it, one did not even "have to be real to be the Doctor". (TV: Extremis)

The promise
The Eleventh Doctor told Clara Oswald that "the name you choose, it's like a promise you make". (TV: The Name of the Doctor) When she reminded him of this and asked what the promise of "the Doctor" was, the Tenth Doctor and War Doctor answered: "Never cruel or cowardly. Never give up, never give in". (TV: The Day of the Doctor)

Before regenerating, the Twelfth Doctor addressed a final speech to the Thirteenth Doctor during which he expounded at greater length, but in similar terms, on the proper code of conduct of a worthy Doctor. He stated as "basic stuff" that she should "never be cruel, never be cowardly, and never, ever eat pears". He added that she should "always try to be nice, but never fail to be kind", and also that the Doctor "shouldn't tell anyone [her] name". His final admonishment was "Laugh hard, run fast, be kind". (TV: Twice Upon a Time)

This was reminiscent of the advice the Twelfth Doctor had given to Clara Oswald while parting ways with her: "Never be cruel, and never be cowardly, and if you ever are, always make amends… Never eat pears". (TV: Hell Bent)

The "Shadow World" Doctor cited as essential features of being the Doctor that one "never give up" and "always trick the bad guys into their own traps". (TV: Extremis)

recalled that the Doctor had chosen his name on the basis that it meant a man "who makes people better". He deemed this to be "sanctimonious". (TV: The Sound of Drums) "Never cruel or cowardly. Never give up, never give in."

- "The promise"

"Doctor of War"
Although, on Gallifrey, the name of "Doctor of War" was bestowed on the Time Lord known as the Doctor owing to his actions in the Last Great Time War as "the Warrior", (TV: Hell Bent) the term as understood by the Testimony was broader and applied to all of the Doctor's regenerations following the First Doctor. According to them, "the Doctor of War" had "walked in blood through all of Time and Space". The First Doctor initially misunderstood and rejected this characterisation as running contrary to everything he understood about his identity as "the Doctor".

However, after he witnessed his future self the Twelfth Doctor adjusting the timeline so that Archibald Hamish Lethbridge-Stewart did not die at Ypres during World War I, he stated that he now understood "what it [meant] to be a Doctor of War". As the Twelfth Doctor joked, "the universe generally fails to be a fairy tale... but that's where we come in!". (TV: Twice Upon a Time)

Relationship to other "doctors"
Relative to a small-d "doctor", the Fourth Doctor that he was "the Doctor... the definitive article, you might say". (TV: Robot) The Twelfth Doctor and the First Doctor, as part of a similar phrase, both went one step further and claimed that they were "the original" or "the original article". (TV: The Doctor Falls) Indeed, according to River Song, the term of "doctor" for "wise man" or "healer" had been involuntarily introduced to Earth's languages by the Doctor through their ever-increasing prominence in Earth's culture caused by their frequent interference in its history. The term "doctor" had similarly been introduced to many other cultures across the universe, always with similar meanings. (TV: A Good Man Goes to War)

Linguistic drift
Because the pattern of the Doctor's actions did not always match their intended code of conduct, some peoples in the universe were mistaken about the intended meaning of the name of "the Doctor". Because of the Doctor's reputation, the natives of the Gamma Forests believed that the word "Doctor" meant "great warrior", and thus they saw war as essential to the identity of the Doctor. The Eleventh Doctor was shocked to learn this during the Battle of Demons Run, (TV: A Good Man Goes to War) and it ultimately inspired him to try and quell his growing reputation, (TV: The Wedding of River Song) deleting himself from every database in the universe. (TV: The Angels Take Manhattan)

"Dr Who"
The being most associated with the name of "the Doctor" travelled in a TARDIS resembling a police box. (TV: An Unearthly Child, etc.) Although they also used the moniker "Dr Who" in their early life, (COMIC: The Klepton Parasites) having allegedly "chosen it to sound mysterious", (TV: World Enough and Time) they already called themselves "the Doctor" when they left "home", but "it was just a name" to them. It was only after going to Skaro and facing the Daleks, whom they saw as an incarnation of the irreducible evil in the universe, that they "understood who [the Doctor] was". From that day forwards, to them, "the Doctor was not-the-Daleks". (TV: Into the Dalek)

"The Doctor" was an ideal they held themselves to, rather than a name they truly applied to their self. When writing their memories, the Doctor would alternate between using the first person for thoughts and feelings of a personal or "un-Doctorish" nature, and the third person to talk about the actions of "the Doctor". (PROSE: The Day of the Doctor) The Twelfth Doctor once stated that he "couldn't be the Doctor all the time", (TV: Hell Bent) and, when raging against Mayor Me, threatened that "the Doctor [was] no longer here: [she was] stuck with [him]". (TV: Face the Raven)

Indeed, upon regenerating with the intent that his new incarnation would break the Eighth Doctor's vow not to get involved in the Time War, (TV: The Night of the Doctor) and "break the promise," (TV: The Name of the Doctor) the War Doctor declared that he was a "Doctor no more". (TV: The Night of the Doctor) He angrily refused to answer to the name of "the Doctor" throughout his life, believing that he had "lost the right" to call himself that after all the terrible things he had done in the name of "peace and sanity".

However, the Moment observed that he still thought of himself as "the Doctor" in his own head, out of habit. Ultimately, the Tenth Doctor judged that the Warrior having had to try and make the right choice on the Last Day of the Time War, when it "wasn't possible to get it right," meant he "was the Doctor more than any of [them]". Additionally, after his future selves helped him find a way to save Gallifrey rather than burn it, he himself declared that "for now, for this moment, [he was] the Doctor again", a feeling which delighted him despite the knowledge that his memory of it would fade, and he would live out his next few regenerations under the impression that he had in fact destroyed Gallifrey. (TV: The Day of the Doctor)

"The DoctorDonna"
After a freak Human-Time Lord Meta-Crisis transferred the Tenth Doctor's mind and memory into her own, Donna Noble briefly became a hybrid being, with the Doctor's brilliance magnified by her human "gut instinct" and some of Donna's own skills. Though taking on some mannerisms of the Tenth Doctor, this "DoctorDonna" remained Donna Noble in mind and body. However, Rose Tyler ruled that she counted as "the Doctor", noting that she, the original Tenth Doctor, and the Tenth Doctor's Meta-Crisis clone (who shared his memories but not his Time Lord biology), made "three Doctors". Before long, however, the Tenth Doctor had to reverse the transformation by locking all of Donna's memories of "the Doctor" away, returning to her to who she was before she even met the Tenth Doctor. (TV: Journey's End)

Jackson Lake
Jackson Lake was a human from the Victorian era whose brain was pumped full of information about the Time Lord known as the Doctor shortly after he had witnessed the death of his wife. With his mind entering a "fugue state", the delusional Lake rejected his name and presented himself as "the Doctor" and a Time Lord, though he had little of the "real" Doctor's scientific knowledge. He built himself a "TARDIS" in the form of a primitive hot air balloon.

When confronted with the Tenth Doctor, who helped him realise his true identity, Lake collapsed in despair, seeing himself as "nothing but a lie", but the Tenth Doctor disagreed. According to him, for as long as the fugue had lasted, Lake had truly "become the Doctor", noting that the bravery and inventivity he had displayed were his own, not a delusion brought on by the infostamp. Ultimately, after Lake fully recovered his faculties and resumed a more normal life, the Tenth Doctor told him: "Jackson, if anyone had to be the Doctor, I'm glad it was you". (TV: The Next Doctor)

Clara Oswald
Clara Oswald, a companion of the eleventh and twelfth incarnations of the Time Lord "Doctor", went by "the Doctor" on several occasions.

After creatures from a two-dimensional parallel world interfered with the TARDIS's exterior dimensions, trapping the Twelfth Doctor inside, he passed his sonic screwdriver onto her and told her to investigate in his place. To his initial annoyance, she treated this as a genuine passing of the torch and took on the name of "the Doctor" for the duration of the investigation, acting in all things as she thought "the Doctor" would. She was not impersonating the other Doctor, however; when pressed, she acknowledged her name to be "Doctor Oswald... but you can call me Clara", and she did not claim to be anything other than human.

After the Twelfth Doctor managed to return to the outside world, she pressed him to give him his thoughts on her performance. He eventually granted that she had made "an exceptional Doctor", but stressed that this did not necessarily mean she had been "good", an idea which unsettled her. (TV: Flatline) Clara once again introduced herself as "the Doctor" when trying to trick some Cybermen at the 3W Institute, although in that case, she was impersonating the Time Lord outright, claiming that "Clara Oswald [had] never existed". (TV: Death in Heaven)

After the Twelfth Doctor parted ways with her with parting advice that included the "Never be cruel or cowardly" admonishment, (TV: Hell Bent) a key part of the "promise" of "the Doctor," (TV: The Day of the Doctor) a Clara granted a form of immortality by being frozen in time ended up running away from Gallifrey in a TARDIS with a faulty chameleon circuit, (TV: Hell Bent) mirroring the First Doctor's original flight from his homeworld. (TV: The Name of the Doctor)

"Shadow World" Doctor
While preparing their invasion of the real Earth in the 2010s, a species of powerful beings nicknamed the Monks created a number of virtual realities simulating possible scenarios. They included replicas of everyone on Earth, all with artificial sentient intelligences. In one of them, the replica of the Twelfth Doctor discovered the truth about the world he inhabited.

Facing the Monks in the Oval Office, he offered the rebuttal that "you [didn't] have to be real to be the Doctor" when they told him that "he was not the Doctor" because he "was not real". Telling them that he was worthy of the name Doctor as long as he "never [gave] up" and "tricked the bad guys into their own trap", he helped save the real Earth by emailing everything he'd learned to the real Twelfth Doctor, helping him prepare for the true invasion. (TV: Extremis)

Missy
After he saved her from execution, (TV: Extremis) convinced the Twelfth Doctor that she had "gone cold-turkey from being bad" and "wanted to change," although she warned him that she did not intend to stick to his own "vain, arrogant and sentimental" version of "Good". (TV: The Lie of the Land)

The Twelfth Doctor viewed Missy's ambition of becoming a force of good in the universe as her "thinking she could be [him]", and decided to give her a chance, picking a distress call and seeing how Missy faired in the part of the Doctor — complete with the Doctor's then-current companions, Bill Potts and Nardole, acting as her own assistants. Missy refused to take the "ridiculous exercise" seriously, however, overplaying the part of the "mysterious adventurer in all of time and space" like a cabaret number, and introducing herself as "Dr Who" rather than "the Doctor". It was ultimately demonstrated that the experiment was a "bad idea" when Missy and the Twelfth Doctor's consecutive mishandling of Jorj led to him fatally shooting Bill with his blaster. (TV: World Enough and Time)