Nit picky unimportant detail. I've never seen a U.S. naval base named for a person. Unlike the other services, the navy names bases after locations, sometimes foolishly. For instance, Navy Base San Diego is divided into subdivisions, the largest is "32nd Street Naval Station San Diego". The carriers dock at Naval Air Station North Island, the submarines at Sub Base Point Loma, the S.E.A.L.s train at Naval Amphibous Base Coronado...
So, unless your universe is different (and no reason why it wouldn't be) the navy base would be "Naval Base Avalon" with the main installation being "Naval Station East Port".
And you might consider having a named Admiral in command of the base, and a lower ranking Admiral or Navy Captain commanding the station.
Since you didn't mention an air base or marine camp, the base is probably home to a surface squadron of one or two cruisers, three or four destroyers, one or two frigates, and one or two replenishment oilers. It would probably have a dock big enough for a nuclear carrier but none homeported thier. At any given time, you'd probably have 1/3 of the ships deployed away from the area, 1/3 active in the area, and a final 1/3 undergoing repairs. The surface squadron would have a junior Admiral commanding.
Goodness, I sound like a know it all.