Not sure if this is addressed in the old series:
Suppose that there is this famous Time Lord that invented chess, and one morning he regenerates and no one witnesses it.
How do Time Lords prove to others that they are the same person?
Since the regeneration thing is managed by those High Council guys, I suppose that they are able to verify it somehow. But what about the rest of the community? How can they tell, trivially, if this new face is truly the inventor of chess, and not somebody impersonating him?
I'd imagine that a TARDIS, which is apparently linked to its owner, can serve as credentials. But I doubt everybody has a TARDIS - besides, that's probably not the most convenient way to show people who you are.
And finally, I'm not sure, but it looks like most Time Lords have some sort of tool (like the Doctor's screwdriver, or the Master's deathstick), which I guess is good for credentials - but heck, the impostor could've just stolen it.