Well, there are cases where there is a name with the exact same spelling, as e.g.
Rita in the case at hand, but with an independent and completely different etymology, making it for the purposes here a "different" name, with another meaning then, according to the alternative etymology.
After all
Rita is mostly popular in
Christian countries, and Albania is a predominantely Muslim country.
So I tried to find out something about a native Albanian
Rita with another derivation than the
Margherita one, but was not successful. First, the normal
Rita always gets in the way, and second there is not much material on the net about Albanian names anyway.