Tinker,

AFAIK W. Richards of Liverpool predated Westley Richards historically, but they were and are a small retail business, and not a glamorous name. They didn't model their name to make it appear like Westley Richards, and they seem to have concentrated on getting a small number of budget priced shotguns made in their name for retail sale. I don't think they ever pretended to be the more famous "Richards" business in their history and their name is a mere coincidence, not an attempt at making money off someone else's more famous name.

That said, several other companies did precisely this kind of thing and it happened not just in the UK but elsewhere as well. Victor Sarasqueta's death and his not having a successor saw several "Sarasquetas" spring up and start making guns in Spain, for example.

Good hunting, my friend!