Technically, the verb "at forene" means "to unite" so going from that, a forening would be a union (among other things, of course), just like De Forenede Stater/the United States, and genforening/reunion.
Så lige at du er dansk. "Association" er allerede et af de accepterede svar for union, men mange tak for tippet!
No, we actually use "union" to describe the USSR - Sovjet-unionen. It's also used in Den Europæiske Union - the European Union. If the United States were called "The American Union" it would probably be called "Den Amerikanske Union" in Danish, since "de Forenede Stater" is a direct translation of the United States.