Yep. There are definitely names like that.
Katherine and
Kate,
Francis and
Frank,
Gabriel and
Gabe,
Andrew and
Drew,
Judith and
Judy,
Anthony and
Tony,
Nathan and
Nate.... there are lots of these. I usually like the full names more but there are a few where I don't- for instance I like Rand better than
Randall,
Annie better then
Annabella, and a few others.