Answer: Stinger
The Stinger is a surface-to-air missile used by the United States Armed Forces and famously supplied to the Mujahideen in Afghanistan in the 1980s. Although the Tomahawk is a type of cruise missile, no one had that call sign in the movie.
Stinger is the CAG on the USS Enterprise and he does not like Maverick because he thinks he is too cocky. He is reluctant to send Maverick and Goose to the Top Gun school but has no choice since they are his best remaining pilots after Cougar resigns.
CAG stands for Commander, Air Group and refers to the Commander of the Air Wing aboard a carrier. Although Carrier Air Groups were redesignated as Carrier Air Wings in the 1970s, the commander still retained the title of CAG.
Stinger is played by James Tolkan, who is most famous for playing the principal in the Back to the Future Trilogy.