Yes, but
Nadezda is not the same as hope. One is in English and one is in Russian and they obviously sound very different. And your right that many other cultures use lots of biblical names, but few of them are spelled and pronounced the same way.
Gabriel is one of the few that is. But it's not like we borrowed
Gabriel from Mexico or something. Americans started using it from biblical inspiration on their own. It's rightfully American, just like a name like
Nicephore is considered uniquely French, even though equivalents in other languages (like
Nikifor) exist for this name and it was borrowed from the Ancient Greek
Nikephoros. All languages are related. So you can argue this for any name. But I'm referring to actual names that occur more commonly in
America than anywhere else, disregarding lingual differences.
Nathaniel may be used in Mexico as Nataniel, but that's not the exact same name to me because they are pronounced differently.
Nathaniel, spelled this way, is pretty trademark American in the grand scheme of things.