LO has a few fake Aunts and Uncles but purely because our family is so large and all such as third cousins and such are still very close so it just gets confusing to explain how they are related so for example my mums cousin has a little girl about Brians age so the little Girl is just refered to as his cousin.
Also my cousin was partly raised by my parents so I see him as more of a brother then a cousin so to LO he is his Uncle.
Another one is OH Uncles has a little girl so again they are just refered to as AUNT, Uncle and cousin.
I dont however do the whole friends as Aunts (apart from one work colege that I do as a joke to wind her up)
I know children can sometimes go through a phase of calling their parents by their names when they are a bit confused as to why others do but its certainly not something I would encourage.
To me parents and children are not equals if we where then the child would not need us to teach, protect, guide, encourage, help, nerture them.
I was always brought up with respect for my parents and elders and calling a parents by mum, dad, mummy or whatever is part of that respect.
Plus mummy is a tittle I have battled very hard to obtain and im not giving it up
However I think a personal petname for your parents (not something anyone else refers to them as) can be a very personal affectionete thing, I have called my mum moogie since I was about 10 (it means mother in ferengi from startrek and yes im that sad)