This is an old thread but I thought I would weigh in.
I had been searching for many years for my Mannion family in Ireland. I knew it was Mannion because it was my maiden name! Recently I got a male Mannion cousin to take a Y DNA test. Guess what - we were originally Mangan from Co. Mayo. I have, since then, found documentary evidence to confirm they were originally known as Mangan when they went from Ireland to Scotland. Later they moved to England where they were recorded as Manning/Mannioun/Man(n)ion and Mangan. Different branches of the family kept different versions of the name.
Two things affected these name changes 1) being illiterate 2) the way a west of Ireland accent would sound to an English or Scottish census taker.
I noticed someone mention that an ancestor signed the marriage certificate but but an X on census (or vice versa). We have a signature on 1911 census for my Great Grandfather. I know he was illiterate. A son/daughter or grandchild must have filled in the form and signed the name. I also have another great grandfather who appears to have signed marriage certificate but earlier records show he was illiterate. Sometimes copies of marriage certificates are rewritten by current registrar so you can't always tell which is an original signature. Sometimes it is a photocopy of original.
When you are searching use all variations of the name. DNA tests are really helpful. Remember people didn't always care about telling the truth on official forms.
The Mannion Clan website from Galway is a useful site and includes some Mangans and other variations of the name.
1901 and 1911 UK census records should show the county in Ireland that people came from. Unfortuanely earlier census just showed from Ireland. 1871 often had the county in Ireland.
Finally - I wonder if Mangan and Mannion sounded almost the same?
Cath