The manufacturer names the plane, but that doesn't mean it's adopted by the fleet. Therefore you'll see aircraft with two names (or if you're the F-22 you'll go through Lightning II, Superstar, Rapier, and then finally Raptor).
What I find interesting is how different companies wanted to keep a common theme to a series of aircraft.
Lockheed: "star," such as Shooting Star, TriStar, Starfighter, StarLifter, JetStar, etc.
Grumman: "cats" such as Wildcat, Hellcat, Tigercat, Bearcat, Panther, Cougar, Jaguar, Tiger, Tomcat