McIlhaggar

In Ancestry.co.uk there are 14 references to the McIlhaggar spelling of our name. When I wrote my blog on 12 September I included this spelling in its title. There I should have used Mc Ilhaggar with a space between Mc and I. Inevitably Ancestry has recorded some items twice under both Mc Ilhaggar and McIlhaggar! This applies to the marriages of Elizabeth and Esther both in 1851. Of the rest, seven of the references are to births where in all cases McIlhaggar is given as the maiden name of the mother. An interesting thing is that all seven are registered in Galgorm, Antrim. I presume this was the address of the registration office, rather than all seven babies having arrived in a Galgorm maternity unit! They are as follows:

Barr, male, born 10 Jan 1868, Galgorm, Antrim;
  Father: Matthew Barr;
  Mother: Matilda McIlhaggar;

Samuel Francey, born 4 Mar 1870, Galgorm, Antrim;
  Father: Thomas Francey;
  Mother Jane McIlhaggar;

William Francy, born 7 May 1865, Galgorm, Antrim;
  Father: Thomas Francy;
  Mother Jane McIlhaggar;

Agnes Francy, born 16 Aug 1872, Galgorm, Antrim;
  Father: Thomas Francy;
  Mother: Jane McIlhaggar;

Jane Francy, born 13 Jan 1872, Galgorm, Antrim;
  Father: John Francy;
  Mother: Rachael McIlhaggar;

Mary Ann Fullerton, born 31 Jan 1872, Galgorm, Antrim;
  Father: John Fullerton;
  Mother: Mary McIlhaggar;

Robert Witherspoon, born 11 Apr 1865, Galgorm, Antrim;
  Father: William Witherspoon;
  Mother Jane McIlhaggar.

I know where to fit numbers two to five in my clan Family Trees (all in that originating in Connor Parish) but am uncertain about the other three. Concerning the Fullerton birth I am confused. I have a marriage of John Fullerton to Margaret McIlhagga on 8 Jan 1872 at Connor Church of Ireland. This could well relate to a birth on 31 January 1872. Mary Ann was certainly the name of John's mother-in-law so it looks like the right family, and Margaret did have a sister Mary. So is the mother's name wrong on the birth record of Mary Ann?