Seconding Sinann reply #4. You need to look at original records, not rely on a transcription, which may have been submitted by a user. The ones posted from FamilySearch are following an American naming style for a married woman imo.
Birth registrations on Irish Genealogy.ie (My incomplete transcriptions/summaries):
Registration district: Killala; Year 1873
Child's name: Anne
Name of father: Edward Loftus
Name, surname and maiden surname of mother: Anne Loftus formerly Maughan
Registration district: Ballina; Year 1868
Name of child: Thomas Maughan
Name of father: Anthony Maughan
Names, surname and maiden surname of mother: Ann Maughan formerly Loftus
https://www.irishgenealogy.ie/en I got "internal server error" as well but I have site as a favourite so accessed it that way. Then I got "internal server error again".
Information seems clear to me:
Edward Loftus married a woman called Anne Maughan.
Anthony Maughan married a woman called Anne Loftus.
Have you found their marriages?
You can look for birth registrations of other possible children of those couples on the above civil records site by putting in father's surname and leaving forename box empty and selecting a range of years.
Have you found baptisms for Anne Loftus and Thomas Maughan and/or their siblings? Mother's maiden name was often included in Catholic baptism registers.
I know you have another thread on the family.
