The nickname Cal for Caleb?

Does the nickname Cal work for Caleb? I’m not talking just completely replacing the name full time, but maybe most of the time? Like is it weird to have things personalized with Caleb and say his first and middle name when he’s in trouble or something, but then call him Cal or even Cal with our last name? He was not introduced as Cal when he was born and is almost six months old, but I’m struggling with his name and trying to find a way to cope. But since the sounds are different, idk if it’s so interchangeable like that.. like my daughters name is Gracelyn and I call her Gracelyn Joanne, Gracie, Gracelyn *last name*, etc.. but Gracie is an obvious nickname and the same sound. So wondering if I can do the same thing with Cal for Caleb or if it’s just gonna sound/seem weird? I’m into full names and don’t even want to be doing this, but I can’t come around to the name and feel like it’s too late to change it, and can’t really get my husband on board for that anyway, so I’m just trying to make the best of it.. 😩

What if I’m the only one calling him Cal and everyone else still calls him Caleb? Or what if it sticks to the point where I’m introducing him on the playground as Cal or he goes to school as just Cal.. Is it weird when the teachers see that his name is Caleb? Ah, hopefully someone gets the gist of my rambling lol thanks in advance for any thoughts!