Not specifically Catholic but also Orthodox. The use of Carmel as given name was started precisely as Catholic and Orthodox thing, if later some people hear the name and think that it is nice and use it in relation with the Mount Carmel or just as a random name, that is another thing, but the name in Western world is
linked with Mary. I don't know if historically before 12th c. (the starting of the use of Carmel as Christian given name), among Jews or Muslims, Carmel was used as given name; I don't think so but I can be completely wrong here.
It is the same with Sharon. The name is
Biblical, because this one is the source, even if most of the people don't know that the name comes from the Bible and just use it because of the sound.
People's ignorance doesn't modify the etymology or the history of the names.