If it's a family name I wouldn't alter the spelling. If you don't like the "ah" sound of
Ammon then I'd keep it in the mn position. I dislike mispronunciaitons almost as much as misspellings.
That said, I adore the name
Eamonn /
Eamon. But I can see why you'd want to stick with the family name instead. If you use
Eamonn /
Eamon, just don't try to pass it off as a family name. That's cheating. :-P