Gertrude is out. It would never be used as a full name, and
Gertie and
Trudy are both unacceptable; DH's grandmother (an Afrikaans lady) was, resoundingly,
Gertruida Susannah Maria, but even she went by a nn:
Dollie!
Greer looks ugly. Most names don't. And the sound doesn't appeal either. If you don't pronounce the -r, it sounds like
Greta in Essex. Plus, I'd be happy to use
Gregor for a boy, which also pushes
Greer down the elimination slope.
Hello,
Gretchen! I quite like it as a name in general, and it's certainly the best of this bunch. But IRL I'd be more likely to use
Greta and a whole lot more likely to use
Margaret.