With of the Hammlers who came from Europe in the early migration (1700s), they left Europe as a Hammler, and the first information we have about them in America, they are Hamlers ! This is very typical when your name was what the immigration worker in America could spell and how they interpreted your name when they *heard* it upon your first step into the New World. Some names were totally changed according to what the immigration worker here *heard* as your name. Our family was fortunate that they just dropped one "m" from the Hamler name! Some names were totally changed by what the immigration officer "heard."
It appears that later immigrants, those arriving in the 1800s, somehow retained the spelling of what the name was in Europe: "Hammler." This could simply be a matter of better education in America, stricter language rules (they may have been required to write their name for the immigration officer--if they could write), or a matter of pride in the immigrant who may have refused to go by any other name than the one that he was born with. Or if the change happened long after the immigrant arrived in America, it was just likely a matter of convenience. One less "m" to write in your name. (The pronunciation appears to be the same in Hammler and Hamler.) Then more educated the public becomes, habitually he is writing down his name for people, the more he or she understands the simple linguistic rules of "speaking American," and as public education became required in America, the more the spelling of a name becomes "in granite."
Once in awhile there is a discrete, personalized reason
for a name changing and then being codified. There were two populations of Hamlers in Ohio, for example. I imagine that as the two populations of Hamlers (those who spelled their names with one "m" and those who spelled their names with two "m's") got to know each other, they simply started spelling their name the same!
(Very occasionally name changes occur for highly politicized reasons, but I doubt that this was the case for the Hamlers/Hammlers.)
Kathleen Hamler PurchaseLPurch6636@aol.com