I sympathize with you as I have a great-great grandmother who was baptized Jane but was subsequently known as Ann. Without the 1839 marriage certificate where her father is named, it's impossible to confirm.
That said, looking at the problem from the Hewen perspective you have a number of pieces of supporting evidence that Jane/Ann are the same person:
- Jane/Ann was baptized in Methwold but had children and died in the parish of Northwold, so the Northwold parish wouldn't have recorded her first name at birth and there was no strong reason they needed to question her choice of name (it looks as if Joseph Coote was quite a prosperous farmer so not a risk to the parish in terms of poor law)
- Ann/Jane and Joseph named children Jane and Edward, Jane Hewen’s parents’ Christian names;
- the Hewens were a long established farming family in Methwold and there is no sign of a daughter named Ann in the timeframe you're looking at, but Jane Coote’s death in 1843 at age 71 fits well with Jane Hewen’s baptism in 1771;
- the Hewen and Coote families appear a lot in each other’s legal documents - as well as Joseph and Jane's marriage licence, William Hewen is a guarantor to Joseph Coote’s admon (1819) where his widow Jane is executrix.
https://www.familysearch.org/ark:/61903/3:1:3Q9M-CSN6-M96T-W?i=541&cat=291384.
The spelling of Hewen seems well established in legal circles and both families would be known across the two parishes as they were big farmers in the area, which persuades me that the baptism records of Ann/Jane’s surname are accurate.
From the Coote perspective, the other Joseph Coote of Northwold you mention appears to be the one whose death trish1120 flagged (marriage bond 1782/age 50, death 1795/age 64), so he couldn't be the father of the children born to Joseph and Ann from 1798 on. There don't appear to be any other Joseph Cootes in the area at that time, only further afield in Norfolk/Suffolk.
It's true this is circumstantial evidence but I can't find any strong counter evidence to suggest that there
are two different Coote families involved. Maybe the name “Jane” came to reflect “Ann”’s status better as she matured?!