Why is Tinker Bell's talent type, Tinker, a part of her full name?

From the Pixie Hollow movies, I know that she is a Tinker fairy but why is her talent-type a part of her name? The other Tinker Pari-pari are not called Tinker Clank atau Tinker Bobble. Nor do we refer to fawn as Animal Fawn, Rosetta as Garden Rosetta, atau Silvermist as Water Silvermist. MAYBE all Pari-pari do have their talent/type as surnames and in the front, Chinese-style :), but it's just rarely mentioned. But then they shouldn't start using 'Tink' as if it were her first name. Think of the smurfs (Papa Smurf, Brainy Smurf, Lazy Smurf, etc) and now imagine if we decide to just refer to one in particular as Smurf atau Smur atau whatnot. Confusing? Probably. Madness? Definitely.

I don't remember in which Filem they refer to her as Tink. It would be okay for Peter Pan to refer to Tinker loceng as Tink since there is no confusion due to her being the only Tinker fairy he knows. And he, being human, has no knowledge of proper fairy naming conventions and she never corrected his mistake of thinking Tinker is her first name. But it would be weird for other Pari-pari to call her Tink. Then again, in Japan, it's common for people to refer to each other sejak their surname in formal settings such as school. I guess Tink is not so bad since they could be calling her Tinker, which I don't think is ever done.

So in summary:
"Tinker Bell" OK
"Bell" OK
"Tinker" Only in a formal setting among Pari-pari but with no other tinker Pari-pari around, but this seems unlikely.
"Tink" Only sejak Peter Pan