Here, my nickname was Babs, because it is a diminutive of my first name, but also a reference to Tiny Toon Adventures. Also Anne, due to a song reference.
I also have a diminutive form of my name made by using -ie at the end, but making it the same name as a certain line of dolls. But please, if you use that name, may the flying monkeys save you!
But can I alter it to Babsie?
Yes! That was one of my favorites when I was younger.
My sister and I would also be known, together, as PB&J due to some fun with initials, and sweet pea for her due to same initial fun. My friend, whose name I change but to a similar example, has a long name, similar to Bartholomew. He's pretty happy being called Bart, but some people like calling him Barth, which annoys him.
And I find it fascinating how Mary became Molly (apparently, it was how the name was pronounced at one point in history or another.