Don't discount Fayle, as Frances suggested. Depending on the lady's pronunciation, it is quite feasible that it could have been changed to Fiel on immigration. A lot of Manx people would pronounce the name, depending on the part of the island from which they came, as Fiel, (Feeyl), on the other hand you will get Fell, with a long soft e, or you get the aye sound, where you shape your mouth for a as in face or potato, but sound ee. I suggest the former pronunciation was used, and written phonetically. After all, this is what happened a lot.