I will confess I'm not sure I understand what you're asking.  But if I do understand you correctly, here's my answer, with corrections in red, and stylistic suggestions in blue:

Translating surnames

How do you translate a surname to have the same meaning in another language?
Ex. Петр - Peter - Pete   "Pete" is a diminutive form of Peter.
Иван - Jean - John  Jean can be a man's name in English, but it is usually a woman's name.
and so on

But how do you change or translate a surname?
Черный - Noir - Black   "Black" is a surname in English.  So are Blue (rare), Brown, Green, Gray (or Grey), Ruby (a color between red and purple), and White.
Каменев - Pierre - Stone  "Stone" is a surname in English.  "Rock" is also a surname, but it is less common than Stone.
Петров - Peters - Peterson


thanks