I have a friend with a 'quirky' spelling of a common name. The spelling is weird because her parents had given her a name they made up, but the family patriarch either couldn't remember how to say it or didn't look at it close enough to see that it wasn't actually the name he thought it was. He kept calling her this unrelated common name, and it stuck. So for her it's not that she spells her name weird, it's that everyone--including her parents and even herself-- pronounces wrong.
Some friends of mine are emergency foster parents for the state and at very short notice can and do take in young children from unsafe/abusive/etc situations. One child they received as a newborn infant b/c the mother was a known addict and had illegal drugs in her system when she delivered the baby. (All of her previous kids have also been taken). Drug-Mom did manage to give her child the name of her favorite off-brand soda before Kiddo was taken away. Friend and his wife take to calling their foster kid "Baby Girl" instead.
If it's the off-brand pop name I think you're talking about-- that's an actual, if uncommon, name for people and places. I know one or two girls with the name. It's also the name of the (male) protagonist of one of the Chronicles of Narnia, and googling it just now turned up a character in a John Wayne movie with that name.
ETA: Further googling has revealed the soft drink company was named after a body of water. Of course, all of this is moot if the mother acknowledged she named the kid after a brand of pop, but if that's the case at least she accidentally gave the kid an actual name.