So far the closest I can find to this is Amze and Amse. They are listed in my Dutch name dictionary as variations of Ame
, itself a short form of names with a first syllable going back to the ancient Germanic root amel
, which meant "heroic" or "combative."
Most of the Amish came from southwestern Germany, but many Mennonites, the larger group the Amish are an offshoot of, were from the Netherlands or the parts of northern Germany near the Netherlands.
In any event, this does look like the sort of name that would have originally been a short form of longer names.