doctor who - How do Time Lords prove to others that they are the same person as their past regenerations?

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.

Answer

This has been a matter of some discussion on the Doctor Who Wikia;

In short, Timelords seem to be able to almost immediately recognise each other. On top of that they're capable of telepathy so any lingering doubt could easily be erased by conducting a mind-to-mind contact;

They can still recognise each other regardless of regeneration. This was shown in The Armageddon Factor when Drax was able to recognise the Fourth Doctor and The Twin Dilemma when Azmeal was able to recognise the Sixth Doctor, despite their last encounter being in the Doctor's fourth incarnation.

Given that Time Lords have been shown to have some telepathic ability, it is reasonable to suppose that this is how they recognise each other after regenerations. However, this doesn't explain how the Doctor recognised the Master on television in "The Sound of Drums". It is possible, therefore, that certain other traits are carried from one incarnation to the next e.g. Subtle facial characteristics.