Can’t find a name or make but the design is familiar.

In ye olden times before semiautomatic mechanisms were developed, it wasn’t totally uncommon to essentially weld multiple guns together for increased “magazine capacity”. Double-barrel shotguns are the only form of that which persists to this day, but back in the late 1700’s to mid 1800’s this was considered cutting-edge tech. By combining barrels of different calibers it was possible to make one gun that can serve multiple functions, as in this case which appears to be 4 rifle barrels and one shotgun.

Given the engraving it’s most likely that this was intended to be a showpiece, but it might have been employed for hunting too. Having four rifle barrels means multiple chances for quick follow-up shots on large game, and the shotgun would be employed to take multiple birds from a single flock.