I'm certain that the Doctor sometimes lies about his encounters with historical figure, but I do believe 11 completely when he says that he knows Father Christmas, despite that being the most probable lie of them all. I also headcanon that 12's skepticism of Santa and Robin Hood were both acts for Clara's benefit and his ego.
I watched through all of modern Who with a friend and they complained about 13 name dropping historic figures/celebrities because it all ''clearly never happened'' and insinuated it was out of character for the Doctor... lmao
Its interesting Two had only well two name drops, both very early on. Maybe it was an attempt to distance Troughton's take from Hartnell's; along with the dropping of the historical of basically any sort. I suppose with Three it was a way to remind people he was a time traveler now that he was mostly Earthbound and mostly in (Insert UNIT date here). At which point it just became part of the character.
With the notable exception of Seven. Maybe at first as a way to distance McCoy's take from Colin... but I also wonder given the political leanings of Seven's writers and the greater focus on having the Doctor interact with everyday people it was also an active attempt to move away from Great Men take of history? Or at the very least tone down the idea of the Doctor always rubbing shoulders with the top class. I suppose we may never know.