My baby's name is Alyssa. What is a pet name other than Aly.?

I know it is a very common name but ever since I was a little girl, I knew this was the right name for me to give to my little girl. I call her baby, and sweety and honey, but I want a more personal name that I can call out in a grocery store and not everyone will turn around. Kinds like a real name but not? Please help me out and no negative feedback please. Thanks in advance!