Adam as a forename, amongst all H.groups, is fairly definative as coming from Ballymena, County Antrim. If this Adam was from Salem Co, NJ then they were definately ex Ballymena (just whereabouts is moot-it is the largest H. Irish mob).
The Ben H.s, of which we have a very incomplete tree, were NOT out of Ballymena-although from a number of other Ulster locales in which other H.s were living. We do have them from Paris KY, where the name has died out. At the moment I haven't any contacts from any surviving H. members-possibly on the Paxton/Marshal sides someone remains.