"Irving" in the example doesn't look like part of a binomial. One would expect to see it on the gravestone there if "Maud Irving" was a unit like "Mary Ann" or "Peggy Sue."
It's significant too that Maud Irving Kane seems to be the only "Maud Irving X" known anywhere. There are zillions of "Mary Anns" and "Peggy Sues," however.
I doubt anyone in 1860 would have assumed that "Maud Irving" on sheet music was a two-part given name rather than a full personal name any more than they would today.
"Willie," however, as in "Willie Ware" was indeed a female name or nickname, short for "Wilhelmina."