American Gun Co. was the name H & D Folsom Arms Co. used on the guns they built at their factory in Norwich, Connecticut, from about the turn of the century until just after WW-I, and sold through their store in New York City.
They made tens of thousands of these guns with all manner of
"trade names" on them as well, but American Gun Co. was the name you got if you didn't specify your own "trade name" for your order. By the early 1920s, H & D Folsom Arms Co. reverted to using the Crescent Fire Arms Company name on the guns they produced and sold. Crescent was the original name on the factory in Norwich when the business was formed, as I recall out of the remains of Bacon Arms Co., circa 1892. By 1893 H & D Folsom Arms Co. had controlling interest in Crescent Fire Arms Co.