The new entity, UWM, was created and put under the UW System (which until that time had had only the Madison campus and the extension offices to worry about) in 1956. It consisted of the former Wisconsin State College-Milwaukee (f/k/a Milwaukee State Teachers College, f/k/a Milwaukee Normal School) with its East Side campus, plus the downtown operations of the University of Wisconsin's extension service. So it was a merger, not just a rename; but the main part of the new entity (in terms of student count, hours of instruction, etc.) was the original components of the old WSC-M. But  is the only person I've ever encountered in my life who says that in 1971 "The University of Wisconsin" meant the four campuses together, rather than either the place in Madison, or else the UW System (which latter is normally referred to under that name).