Perhaps this is not the right Mary Ellen as her parents are named in the marriage register so I don't see why her father wouldn't be named on the civil registration.
One possible reason is that he died when she was quite young, maybe she knew her Mam was a widow but didn't know her Dad's first name.
He's on the 1891 census with the family in Soho Street
Piece 2922, Folio 30, Page 10
by 1901, he's not with the family at Upper Milk St., though Mary's Mam is down as being married rather than widowed
Piece 3413, Folio 61, Page 29
Out of interest I searched death registrations/ RC burials in Liverpool and Workhouse Records (workhouse infirmary was the only source of medical attention for the everyday folk) for records 1896+/-5 years.
There is a quite possible George Riley, died in 1896
workhouse records say he was RC , Married, address Upper Milk St., admitted 27 Jul 1896, died same day
Deaths Q3 1896 Liverpool 8b 37 George Riley age 39
Burials Ford Cemetery 31 Jul 1896, George Riley of Upper Milk St., age 39.
Age is a year or so out but that's par for the course, another drawback is that the 1901 census 'says' his wife is married, but maybe the above is worth investigating/checking out, if a death cert shows the death was registered by a known relative that would lend a good deal of weight to the possibility
Boo