aside from names that are those of deities or attributed to a deity or very strong it does not matter.
There are tons of christians in arab countries with arabic names, while they would not name their kid muhammad, there are many with names that we see as names of muslim
Omar Sharif, who changed his name to that, is christian, Tariq Aziz..i know bad example..the former minister of Iraq is chrisitian, the fomous writer khalil Jibran was christian. Many names in iran which we now see as ‘muslim’ names existed before islam and have zoroastrian background, similar situations exist in turkey, afghanistan and even Pakistan.