Yes! I have three cases of this:
A boy from my high school was named Robert, but goes by Buddy- when he was little he used to be "Mommy's buddy", and it stuck.
My uncle used to have a best friend when he was about five who followed him around everywhere, so my grandpa called them Mutt and Jeff (after the old comic strip). Since then my uncle goes by Mutley or Mutt, at least in our family.
And finally, when my mom (Anne) was an infant, she and my grandparents were traveling late at night. My mom was hungry, so they pulled into a diner. The chef had just closed for the night but he had muffin batter in the fridge, and my mom ate a ton of it. Her parents called her Little Miss Muffet, which was shortened to Muffi. Now my cousins all call her Aunt Muffi.
I agree with you about people with names like this being characters. I think sometimes the names just stick! (Sorry this is such a long post!)