I think it's cute.
Libby was our joke name for
Liberty (our dd was due on
July 4th). After discussing it, we actually liked it as a nn for
Elizabeth. I preferred
Bess or
Betsy (to honor
Elizabeth "
Betsy"
Ross, ha), but they're awful with our surname so that's why we briefly considered
Libby. I think I've only known one person named
Libby while I can recall many people named
Lisa,
Beth or
Liz.