John McDowell's sons as so far known:
Thomas Parker McD, born c. 1847
Henry McLorinan McD, born c. 1848
John McD Junior, born c. 1858
In Reply #1, shanreagh suggested trying to exploit a naming pattern to find John's father's name. But shanreagh's pattern seems to be Scottish rather than Irish? Anyway, there's a different naming pattern given on irelandxo.com:
First son named after father's father
Second son named after mother's father
Third son named after father
Fourth son named after father's eldest brother
And so on.
John's son Henry McLorinan McD flipped first and second in that pattern, as I pointed out in Reply #5; his first son (Samuel McMillan McD) was named after the mother's father, and second son (John McD) after the father's father. So the pattern, so modified, might serve as a template for understanding the naming of John's sons.
Henry's third son, another Henry McLorinan McD, was named after his father. Henry's fourth son, Thomas, can be named after his father's eldest brother Thomas Parker McD (no point in preserving the middle name). Fifth son is Alexander: perhaps named after his father's half-brother Alexander Mackey Parker, in a variation from the pattern. Sixth son William, named after ?
John's first son Thomas Parker McD, named after his mother's first husband, is outside the pattern. Henry McLorinan McD, named after his mother's father, is first in the pattern, according to the variation we find in Henry's sons. But the only so far known other son, John Junior, is named as if third in the pattern, after his father.
There is room between Henry McLorinan McD, c. 1848, or better between the two daughters born soon after Henry, and John Junior born c. 1858 for a so far unknown other son, who may have been named, as if second in the pattern according to the family variation as seen in Henry's sons, after John's father.
Could it be a William? Henry's sixth son William could then have been named after the eldest of his father's brothers whose name hadn't already been used.
Sorry this is so complicated. I would be grateful for any comments.