And annoying the language speakers. Pёtr is painful to read. Peter, Pyotr, Peter, Пётр, pick any, but don't mix and match please!

What about the other way? Would it be legit to transliterate the english nickname Pete as Пить?

Много городов у вас в России))

That is how it is done when translating literature, right? Pete becomes Пит - just like you are pronouncing Pete.