Withycombe's Oxford name dictionary lists Jesmond as a form of the feminine name Ismen(i)a. Here is the entry:
"Ismen(i)a (f.): this name is found from the 12th C in various forms. Ismenia occurs in
Ireland as late as 1800. There are some signs that this and the possibly related Ismay (q.v.) may be of Irish provenance and possibly of Celtic origin. It is unlikely that they have anything to do with the Greek
Ismene, the d. of
Oedipus, although
Antigone occurs as a christian name in the 13th C. In the 17th and 18th C Emony, Emeny are found as men's names, possibly a use of the surnames derived from this christian name. The gipsy family of
Heron use Emmanaia as a woman's name.
The name Jesmond which was common in North Lancashire in the 16th-18th C may be the same name. Other forms of it are Jessimond, Jesmaine, Jismond, Gismon."