Is Justin a Muslim's name

"Justin" is a Latin name that means "just" (as in "fair" or "having the quality of justice"). The Romans were never a predominantly Muslim culture.

However, there is no reason a Muslim could not be named "Justin". Muhammad forbade names with bad meanings (unclean animals or inappropriate qualities) or those specifically associated with other religions ("worshipper of Manat", etc.). He did not require converts to change their original names if these had acceptable meanings and connotations.

He probably never met anyone named Justin, but it sounds like the type of name he would have allowed.