You go by a Hebrew nickname here, I don't think there is a problem from Jewish perspective to use a Hebrew name for a gentile, unless a priestly/Levite surname which only descendant of Priests/Levites are supposed to use.
Actually most "Christian names" are based on Greek versions of Biblical names. I was actually wondering about that myself- how come all the disciples got a Greek version to their name (John for Johanan, Mathew for Matai, James for Jacob ...) except for Judas of course...
In Israel most people go by their Hebrew name as their first name, most Sabars don't have a foreign first name at all. For religious matters the name formula is "Jacob son of Yitzhak" or "Jacob son of Rachel" if the person is a Kohen or Levi I think it is added also to the name. For any other matter we use the first name last name formula like in most other western countries.