Gertrude: I find the sound rather ugly, but I love the Shakespearean association.
Gretchen:
Greta is lovely, but
Gretchen is dreadful.
Greer: interesting, and I like it, but pronounced GREER. GRIR sounds rough to my ear.
In short, I'm torn between
Gertrude and
Greer, but I think I prefer the latter.