We gave dd2 a more "traditional" name but like lulumama's daughter she has been known by the cuter version since she was very tiny. She wouldn't even know her real name tbh (it's not lulu/lucy btw but a bit similar)
Sometimes I think we should have just given her the shorter form, but it is a name like MrsB says might become a bit cutesy. If she wants to change back to her more sensible name when she is older then that would be fine with us.
In this case I absolutely love the name Lulu though.