I can't see purposefully setting out to name a child Grace and using the nickname Gigi. I can, however, see the nickname developing naturally. I mean, I know a Whitney called Wendy and a Kelsey called Lucy their parents didn't set out to be call them those things, they just started as childhood nicknames and stuck.
not expecting, enamoredhttp://www.behindthename.com/pnl/138517http://www.babynames.com/namelist/9750188