My understanding for the SSA (US Social Security Administration) is that hyphens are omitted, and double names without a hyphen are recorded as first name, middle name.
So Mary-Jane would be recorded as
Maryjane, and
Mary Jane would be just
Mary. The SSA doesn't include any middle names in its popular-names listings.
Informally, I have observed that double names without a hyphen are very common, more common than the hyphenated versions and often more common than the combined versions:
Mary Ann,
Mary Jane,
Mary Lou,
Ann Marie,
Jo Ann,
Jo Ellen, etc. These would have been counted as
Mary,
Ann,
Jo. I think this helps explain why a name like
Jo was so high on the list through the 1960s.