I seem to remember a Sliders episode taking place on an Earth that was ruled by a state called the Human Hemispheric Alliance. I thought that was a pretty cool name.
That said, the 'United Federation of Planets' is by far my favorite name for a government. It's simple, efficient, not linked to any particular race or planet, and (perhaps most important) not burdened with any of that ridiculous 40's/50's pulp crap that we always used to hear about, things like Space Command or Star Service or anything like that.
On the other hand, the Alliance from Firefly could have been named better. 'Union of Allied Planets'? Well, DUH...it's a union, of course they're allied!![]()
Side note: I thought it was kind of funny - and just a bit too convenient- that all five major governments in Babylon 5 just happened to have different names. Earth ALLIANCE, Minbari FEDERATION, Vorlon EMPIRE (yeah right, like there's anything about the Vorlons that even remotely qualifies as imperial), Narn REGIME, Centauri REPUBLIC (now why didn't JMS call them an Empire? They obviously were one... ) Wink wink, nudge nudge.
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You could just as easily say 'of course they're united, they're a federation', though.