To be more specific, can the Abrahamic faiths be separated from their nationality?

The origin of these religions is said to be in the Middle East (correct me if I'm wrong) . I thus wonder if the package of Islam or Christianity can ever be independent of these certain cultures that gave birth to them. Is not the heritage of the Quaran and the Bible, Middle Eastern?
For example, if a newly convert assumes Islam do they also simultaneously adopt facets of Arabic culture?
. . .Muslims carry Arabic names, Christians wear Hebrew names.

So when one adopts any of these religions does such a person also partly assume another culture?

And does that mean certain religions are biased to particular cultures i.e. does Islam favour and lean more to the Arabs?