I mean, really, there's nothing you could call it that doesn't sound pulp-y. I mean, really -- "Star Fleet?" "Space Force?" "Space Command?" "Star Command?" "Extrasolar Command?" Etc.
I mean, if you follow the name construction of the aeronautical military forces of most countries -- "Air Force" -- and apply it to space, what do you get? "Space Force." "Star Force." Etc. It sounds a bit silly. I'm sure that to people living in 1887, the term "Air Force" would have sounded ridiculous, too.
Science fiction writers have used "Stellar Navy" which I rather like and have used for my own short fiction. It works, without such prefixes as Intra- or Inter-.