So am I correct in thinking that John Soper & Martha Hunt married in 1768? Was William Hunt her father? The couple married by licence and Martha's age is given as 21. She may have been a little older, but John's age is given as 24 so I think it is likely to be reasonably accurate. Why do you think her name was different at birth? There is a baptism in Kingsclere for a Martha Hunt on 27 Feb 1746/47, parents William & Hannah. Is this likely to be her?
William Hunt baptised 17 Feb 1713/14 was the son of James & Elizabeth, but I cannot find a marriage in Kingsclere or surrounding Hampshire parishes. There was a daughter Elizabeth baptised in 1712, another daughter Joan in 1718, son Stephen in 1721, Mary in 1727.
There is a baptism for a James Hunt 20 July 1684, son of William & Joan Hunt at Kingslcere. William Hunt married Joanna Hynd 23 June 1678 at Kingsclere.
There were a large number of Hunt families baptising children in Kingsclere so it is important to ensure that you investigate any burials as well to see which children survived.
I can find a William Hunt baptised in 1652, son of William, no mother named. No other William in the 1650s that I can see. Since this is the Commonwealth period, the completeness of the records cannot be guaranteed.
A Thomas Hunt, son of Thomas Hunt was baptised 24 April 1631 at Kingsclere, no mother's name mentioned.
It is quite unusual to find two forenames given to people in the 17th century. And I can find no marriage for Elizabeth Jessup to anyone named Hunt in Hampshire.
I'm not sure where the USA fits into all this.
Nell