I think the manufacturer get the honor, but i don't know who exactly... There's usually a theme the manufacturer's follow, like DeHaviland names their planes after incects, Lockheed in a celestial theme, etc...
Then again, the service requesting the A/C may have a requirement, like the army insisting that all its choppers be named after indian tribes (Comanchie, Apachie, Kiowa, etc..). On the other hand, sometimes the name given by the soldiers who use them just stick... i.e.: UH-1 Huey.
Just rambling. Feel free to correct me.