Hi
my name family name is Lorenzo.. quite common... and also it is my name.
I don't know the meaning of Lorenzo, indeed I've neve been interested about that and, by the way, it doesn't give - in this case - any information about my family, like where we were born, any connection with professions and that sort of things.
When I meet people for first time and this happens at work I introduced myself by saying my name and my family name but when a meet people with my friends I just say my name.
About pet names I use "vida" and most of the times I use "diminutives" for pet naming.
That's all, thank's !!
Laura