You can iterate over the values:

function GetAnimationNames(Animation anim)
	// make an Array that can grow
	var tmpList : Array = new Array();

	// enumerate all states
	for (var state : AnimationState in anim) {
		// add name to tmpList
		tmpList.Add(state.name);
	}
	// convert to (faster) buildin array (but can't grow anymore)
	var list : string[] = tmpList.ToBuildin(string);
	return list;
}