Statewide vital records prior to September 30, 1907 are at the Wisconsin Historical Society, www.wisconsinhistory.org/vitalrecords/
. You can view the index of the record there. According to Wisconsin law, you can't look at the entire record online without purchasing it.
I can't explain the descrepancies in the names except my German ancestors had three names before their surname. Pauline E. M. L. makes sense to me that she was called or used the name of Louise Mueller.
I'd explain the name differences in the Notes field of your genealogy software program. Successful Searching!