This story is a sequel to War of the Unfoals
A name is more than just a word. It's an identity.
So when you pop into existence at the age where most other ponies have one, you realize that you need one yourself. Which poses a problem for those who's parents never had them.
After all, ponies with identities don't become unfoals.
And for one colt, getting a name from his parents might not be quite so simple...