The most important relationship was with the unit you were in. That's where your roots were. Not the place you were at.
Every military unit in existence today has only been associated with the United States. Units move from post to post on a regular basis depending on the needs of the service.
Having a military base named after a person should be reserved for men who kept the faith with the United States.
I think that's reasonable. I also think if it were possible to ask the namesakes themselves that they would not argue the point.
There is a possible notable exception I'm aware of (I don't know when all the bases were named, just the ones I was stationed at). Ft. Bragg was named before the civil war started.
It's much easier to figure out what to do with a few instead of a bunch.