I have to admit I too struggled with this question for years. The spelling variations (Harrower vs. Harroway) bothered me. The court records relating to Alexander after his death, and referring to his orphan sons Merryman and Charles, used only the spelling Harrower. What if, just by chance, there is a Harroway family in the area that also named their sons Merryman and Charles? Slim odds I know, but I wanted to be sure. If Alexander was not their father, researching his family would be barking up the wrong tree - a big misdirection I preferred to avoid.
The proof that Alexander Harrower is indeed their father is found in two court documents entered about 16 years after his death, both dated 19 Nov 1756:
The first is from Lancaster County, VA Will Book 15 (1750-1758) where Merryman and Charles settle with the administrators of their father's estate. Notice the surname is spelled Harroway. The second is from the same county, referring to the same event (ordering payment on the estate settlement), and recorded on the same date but in Court Order Book 11 (1756-1764). Notice it refers to the same family but with the spelling Harrower.
With these two records referring to the same family but with spelling variations Harrower and Harroway, I am now confident Alexander Harrower is the father of Merryman and Charles Harroway.
As far as I know, this is the first time the Harroway spelling appears in our family. Was it simply a phonetic variation that stuck? Merryman and Charles were young men at the time. Did they decide to change the spelling for some reason? We will likely never know.