Gabriel has only ever been shortened to Gabe . . . maybe when he's older the Gay part might happen, but meh. It's hard enough that Gauge/Gage is common in our peer group and often it is uncertain who is being called over.
Most of our animals have had distintly animal-sounding names (mama kitty, Bing, Freckles . . ) so a kid and a pet sharing a name would be unlikely.