He always was paranoid about people meeting their time-copies. It's not really a rule, though; there have been several Doctors in one place on at least four occasions, and the Doctor was in the same time and area as his past self in the same regeneration on at least two more.

When dealing with multiple versions of the same character, or multiple characters that go by the same name, it would start getting even more complicated than Doctor Who inherently is. For example, there are three separate characters that call themselves the Dalek Emperor, one of which is the same character as Davros, the Fourth Doctor's main villain and creator of the Daleks, after one point in his life, but not he's not permanently the Emperor after that point.
How would someone even deal with that? Would there be two versions of Davros, the Emperor and the wheelchair-scientist? Would the two be constantly fighting over who the "real" Davros is? Would we have a second Dalek Civil War between the Vault Daleks and the Imperial Daleks for the validity of the Davros name?

I tried to make a situation that sounded complex and unwieldly, but that could actually be a pretty cool recurring scenario if it was written right. Hmm...