Post-regenerative amnesia

Post-regenerative amnesia was the loss of memory which was a common-side effect of traumatic regenerations. Symptoms ranged from uncertainty about names, (TV: Castrovalva, Time and the Rani, Deep Breath) including their own, (TV: The Woman Who Fell to Earth) forgetting a skill they had mastered, (TV: The Time of the Doctor) to complete memory loss. (TV: Doctor Who)

The Doctor
Whilst claiming to be the Sixth Doctor's successor, Jack Harkness excused his ignorance by claiming to have post-regenerative amnesia. (AUDIO: Piece of Mind)

Following his regeneration from the Sixth Doctor, the Seventh Doctor suffered from post-regenerative amnesia which was exploited by the First Rani, who used the opportunity to disguise herself as the Doctor's companion, Melanie Bush. (TV: Time and the Rani)

Immediately post-regeneration, the Eighth Doctor had few memories, unable even to recall his own identity. (TV: Doctor Who) He sought out Grace Holloway, whom he believed would know who he was. (PROSE: The Novel of the Film) While taking a walk with Grace, the Doctor recalled an early memory of a time on Gallifrey with his father. He soon remembered he was called "the Doctor", and kissed Grace at the revelation. (TV: Doctor Who)

The Eleventh Doctor briefly forgot which way was left and right shortly after his regeneration. (TV: The Eleventh Hour)

The Twelfth Doctor suffered a brief memory loss immediately following his regeneration from the Eleventh Doctor. The most immediate concern was that he forgot to fly the TARDIS, (TV: The Time of the Doctor) leading it to land inside a tyrannosaurus rex which was deposited to Victorian London as a result. Disembarking, the Doctor initially failed to recognise his companion, Clara Oswald, to the point of mistaking her for Handles, and confusing Strax with Clara. (TV: Deep Breath)

The Thirteenth Doctor was initially unable to identify herself, though she was able to recall being a "white-haired Scotsman". However, following a confrontation with Tzim-Sha, she was able to remember that she was the Doctor, observing that "a bit of adrenaline, dash of outrage, and a hint of panic knitted [her] brain back together." (TV: The Woman Who Fell to Earth)

Concerned that her successor might experience post-regenerative trauma, the Thirteenth Doctor composed a guide about their life. (PROSE: A Short History of Everyone)

Others
Lily, the fourth incarnation of a Proto-Time Lord, did not remember her previous lives. She was ultimately killed by the third Lake, who was mortally wounded by River Song in retaliation. To River's shock, she saw Lake regenerate into Lily, and was forced to send her back in time to meet her fate. (AUDIO: The Lady in the Lake)

Behind the scenes
The comic pitch Doctor Who: The Last Regeneration had its exclusive, newly regenerated incarnation of the Doctor suffer from post-regenerative amnesia, only recalling his identity when the TARDIS materialised before him.