Mary McGrath or Mary Magrath

Mary was born in Mayne, Westmeatharound 1810. We have searched the Irish Catholic Parish Registers and found a Mary, born March 6, 1808 to an Arthur Magrath and a Peggy Fagan. In checking these records from 1800 - 1812, there are 3 notations for Arthur and Peggy but also for Arthur Magrath and Margaret Fagan. Would it be likely that Peggy and Margaret are the same? There are only 2 Marys recorded and the other was born August, 20, 1806 which seems a little removed from 1810. By the way, almost all the Magraths were found in Coole but as I understand that is still in the parish of Mayne. I also found an Arthur who died December 1, 1846 Coole, Westmeath and this date would seem to fit with someone having children between 1800-1810. I could not find any death notations for either Margaret or Peggy however, I did find a Margaret that attended a death bed confession with another woman named Scott. I don't recall the date but think it was in the 1820s or 30s. I found no marriage recorded for them. Can you help? Would just like to confirm as much as possible that Fagan is the mother's name.