Bellmore Gun Co. is one of the myriad "trade names" found of the cheap sidelock doubles produced by H & D Folsom Arms Co. of 314 Broadway, New York City, at their gun factory in Norwich, Conn. The guns Folsom made there were marketted by them under the American Gun Co. name prior to WW-I --
and Crescent Fire Arms Co. name after WW-I --
Many other purchasers also got American Gun Co. and Crescent Fire Arms Co. marked guns if they didn't specify a "trade name" of their own. I don't know, off hand, who used the Bellmore Gun Co. name. I bet there is a good chance Drew Hause will know.