I'm not a pilot, I was enlisted USAF for a single four-year tour. But I believe that call signs are bestowed upon the recipient, the aircrew does not get to pick their own.
And as you move from duty assignment to duty assignment, your fellow aviators may give you a new call sign at any time...
You're correct. Usually it was the result of a play on your last name like "Master" Baden, or something notorious you did in the past. Sometimes it was a distinguishing characteristic.
We had a guy named Dick Smith, his call sign was "Limp"
One guy with the last name Bright was "Notso"
Another guy who was losing most of his hair was call sign "Chemo"
Another who's last name started with PECS, his call sign was "tits"
Another who had overstressed two jets by pulling too hard was call sign "Yank" because of it.
One who had accidentally set himself on fire while drunk at a party was "Torch".
You get the idea. Call signs like Maverick and Ice Man are for the movies, in reality it was usually something designed to poke fun at you.