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
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)

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.