There never was a "Union Army" as an official designation. It was officially the "United States Army." Whether calling it the "Union," "Federal," "National," or "Northern" Army - all of which were used in varying levels of popularity, the only official name was "United States Army." The volunteers were designated "United States Volunteers" not "Union Volunteers." Therefore, the "Union" army didn't disappear in 1865, the United States Army simply shrank as men mustered out and it was reduced to peacetime size.