Ancestry has very little (almost nothing) for Irish records- it's better for tracing families after they've left Ireland and gone to U.S., Canada, etc.
Online family trees can be quite unreliable and I'm doubtful that a woman having children in 1860s Co. Antrim would have the first name of Kelly.
Civil registration index has one birth in 1860s for a John Gaston in Co.Antrim - 1865 Balymena reg. dist. vol. 11 p.150. However, according to I.G.I. (
www.familysearch.org) he was born 7 June 1865 son of John Gaston and Margaret Hasty.
Possibly your John Gaston was bron before registration started in 1864.
Ulster-Scots naming pattern is first son after paternal grandfather, 2nd after maternal grandfather, etc. but many families didn't follow this. Middle names are trickier. Sometimes the child was given the complete name of the person (such as Stafford Church for his grandfather) but other times the first name and the middle name have no connection. Surnames that are used as middle names can come from mother's/grandmother's/etc. maiden name, local minister, doctor, teacher, landlord, etc.
Just wildly guessing here- perhaps John Gaston's mother was McKeen and
Elizabeth McCartney's mother was Ferguson.
Just found in IGI a Stafford McCartney born 1 Apr.1871 Co.Antrim to Stafford McCartney and Elizabeth McDowell. Other children-
1. Mary born 13 Jan.1864 Galgorm dist., Co.Antrim (p.100 in civil register)
2. Elizabeth born 19 Feb.1865 Galgorm dist. (page 152 in civil register)
3. John born 22 June 1867 Galgorm dist. (page 134 in civil register)
4. Mary born 1 Feb.1870 Co.Antrim
5. Martha born 1 Jan.1877 Co.Antrim
