Help: Moria 

Hello, something is bugging me about Moria, and you might be able to help.

The inscription on the doors reads 'Ennyn Durin aran Moria. Pedo mellon a mino'. Now why would they refer to it as 'Moria' when it didn't get called that until later 3rd age? Am I wrong in assuming Moria was a later name or is it an authorial mistake?