> The two names can co-exist

That's what I'm wondering the most actually.

I think the least intrusive way to do it is to introduce a literal clone of the product under a different name. Make it clear that it is the exact same things as the original.

What I can't find is any examples of anyone doing this. Also, not sure how would the mighty Google react to these shenanigans and if their automata won't decided to delist both products just because it looks fishy.