Nosterfield sounds like a contraction of Paternosterfield from an ecclesiastical connection. Thorn being a giant my suggestion would be that Tanfield is really Grimstonfield. Purely guesses however.
Isn't "Noster" Latin for "our", hence "pater noster" = "our father", so maybe Nosterfield is just "our field". On the other hand maybe it's related to "north" or "northern" as in "northerfield".