When I was in flight school about two years after this incident Mark Baden was one of my instructors. He was a good guy and his call sign was “Master”.
“Master” Baden. That was back when you could have cool call signs. I doubt that would go over in todays Navy.
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...