Considering the real-life U.S. Navy uses primarily 'Fleets', 'Task Forces', and 'Strike Groups' more often than pretty much anything, I feel one of those three would probably fit better. To my knowledge, Liberty still has three entire fleets that haven't been expanded on (2nd, 4th, and 7th), four (6th) if you don't count anything that Mr. Mike did, and could have any number of Task Forces, Strike Groups, or however named divisions within the Navy that could be built on. Food for thought, though I'd personally be against naming anything with an American legacy an 'Armada', as that's really a European thing.
Continuing to use van Leer as a character is, of course, your decision, as the community standards permit, but considering both the rank he was stripped of and the one he holds now being considerably disproportionate, as well as 46th, an official faction, giving the discharge RP, it really throws a wrench into any consistency your character would have, not to mention pretty much voiding the RP of van Leer's actual departure from 46th as a whole.
I'd highly recommend using a new character, and if you really do have a firm interest in using van Leer, maybe make him an advisor for 1st's operations. It's still a stretch, but it would at least be more consistent character development than the discharge disappearing and him magically becoming an Admiral.
I've gone through a discharge myself, under honorable conditions, and seeing this kinda irks me in a spot I don't like to be reminded of.