Well, no, Rydia *is* Rydia... not the whole "L's are R's" thing... nonono. [keeping it FFIV] Kain is Cain, and Milon's original name is Scarmiglione. Things like that.
Well I have a Final Fantasy artbook by Amano (which I purchased long after I originally played FFIV... I was seriously a kid back then) and it has her listed as "Lydia". I'm assuming that's legit considering it's officially licensed merchandise.