Hi Mark ...
I think I may be able to help you - or possibly confuse matters even further!
An AKERMAN marriage on the OMI (the only likely one in terms of location and time-frame) led me to the Handborough PRs. Between Woodstock and Handborough is the parish of Blenheim Park, which has no registers. Here's the marriage:
20 JUL 1783 - Moses AKERMAN & Jane HUNT (both made their mark)
I then found these baptisms:
21 AUG 1785 - AKERMAN (blank), d. Moses & Jane
20 APR 1788 - AKERMAN Rebecca, d. Moses & Jane
18 JUL 1790 - AKERMAN Ann, d. Moses & Jane
I would think it definitely possible that the eldest daughter was named after her mother.
This was the only burial on the registers:
21 JUN 1816 - AKERMAN Rachel, 20, from Blenheim Park, parishioner
There was also this baptism:
27 APR 1726 - AKERMAN George, s. (blank), woman wanderer (perigrinats)
(A "perigrinate" is a person who walks from place to place, usually on foot!)
It's possible that George could be Moses' father, although I can find no marriage for him on the OMI and no burial for him at Handorough.
Hope this is of some use!
Pennie