Burges(s) is her maiden name, Her baptism and those of her son (also John) were at Gee Cross Unitarian, Hyde, Cheshire. She is reported as Jenny when her son is baptised but there is a Jane in the 1841 census living next door to John and Martha (she was Ashworth and we have all the details on them) in Compstall (the 'we' is my 3rd cousin Dot-I'm also Dot- in USA and 3rd cousin x2removed in Ireland)
Jane who is in Compstall in 1841 census has 3 daughters whose names all repeat in subsequesnt generations PLUS 2 of these daughters were baptised on the same day as their Nephew (my gt grandfather) all were non-conformist baptisms.
I hope that helps.
Dot