Bradley Walsh (in-universe)

Upon seeing a stained glass window depicting Graham O'Brien, the Thirteenth Doctor said that it was "either [Graham] or him from the gameshow". (PROSE: The Good Doctor)

The actor also appeared in the BBC television series Doctor Who, (WC: The Zygon Isolation) which the Doctor was aware of. (PROSE: A Letter from the Doctor, Bafflement and Devotion, TV: The Doctor Appears, et al.)

Behind the scenes
This character is clearly intended to be an in-universe Bradley Walsh, but his name has not been stated in a valid source.