David Tennant (in-universe)

David Tennant was an actor who portrayed "Doctor Who" in a television programme of the same name, and was considered by the Twelfth Doctor to be one of the greatest actors on Earth. He was brought together, along with many other actors to portray "Doctor Who", for a special breakfast in "London's glittering West End". The Twelfth Doctor considered making an appearance, to "see what these fictions [were] like." (WC: Peter Capaldi and Simon the Shy Cyberman Invite You to Breakfast with 7 Doctors)

In 2005, following the Dummy Massacre, Steve Woolfall responded to whoisdoctorwho.co.uk's request for sightings of the then missing Rose Tyler, reporting that he had seen a girl that looked like Rose in the Grosvenor Museum in Chester that afternoon with a chap that reminded him of "that Casanova bloke". Steve suggested that it might not have been the same girl but that it was strange nonetheless. (PROSE: The Doctor Was Involved in the Dummy Massacre)

Behind the scenes
Evidently, "David Tennant" here was intended to be an in-universe version of the real David Tennant, who portrayed the Tenth Doctor. Although he was not given a clear in-universe illustration during the narrative of WC: Peter Capaldi and Simon the Shy Cyberman Invite You to Breakfast with 7 Doctors, the end of the webcast included a screen featuring photographs of each Doctor who would be present at the event, in-costume as "the Doctor". If taken as an in-universe representation of Tennant, this qualifies as the only in-universe illustration of the character outside of parodies.

Information from invalid sources
David Tennant had a mole called Daniel. When he showed him off to Billie Piper, she freaked out. (NOTVALID: Doctor What 5)

He filmed a scene from New Earth with Billie Piper, during which the design department tested out their plans to have "ultra-realistic" cat people. (NOTVALID: Doctor Whoah! 370)

In October 2007, he filmed a Children in Need special alongside Peter Davison. (NOTVALID: Doctor Whoah! 388)

While on tour with the Royal Shakespeare Company, Tennant was forced to sign every issue of a fan's extensive Doctor Who Magazine collection, driving him to exhaustion. (NOTVALID: Doctor Whoah! 400)

When Jack Harkness was fighting Sao Til, he reminded the two that they were no longer filming. (NOTVALID: Tonight's the Night)