1) 가비 or 게이비 ( but this name does not give any sense, it looks like a grey building or someting like a foreign machine ) I recommend 깨비 or 깨비^^ as your nick-name, because It would recall your name, Gabby and it seems unique. 깨비 means a sprite. But it gives an impression of something cute,interesting. I know that I'm very poor at Enghish. but, I am sure that you could catch my words...... I hope.....^^;;

Gabby in 한글 would be 개비. ^^

This is a late reply but my name is Gabby too and I use 가비.

가비/개비 is about as close to "Gabby" as you can get. Although, 개비 is more or less "Gaeby" sound.