Happy Name Day is correct.
happy name day
Happy Walters's birth name is Happy David Walters.
Happy
Happy Dave's birth name is David Haskell.
Happy could be considered a name. In reality one could name a person anything he wanted to.
Happy birthday to you Happy birthday to you Happy birthday dear (person name) Happy birthday to you
Happy Feller's birth name is James Patrick Feller.
Happy Humphrey's birth name is William Joseph Cobb.
Happy Felton's birth name is Francis J. Felton.
Happy name day = Bon Fête de noms
The Happy Show