Yes, they're Dominican Cohibas.
They make cigars all over Dominican. You can get someone to roll you one pretty much anywhere. I have a couple I got in Punta Cana and have seen the ones you got in gift shops.
That said, they are what they are. I smoked a couple Dominican home-rolleds while I was there and they were okay. They were super wet, but they're supposed to be super wet when you just rolled them.
My suggeston is that you smoke one right away so you get that same soggy experience. It's fun. Then set them back and try them again later. They might be good, maybe not.
They don't really mean any harm down there in using the "big names". They use them jokingly. I saw 100 Walmarts that were junk stores. Right next to our resort was a string of shacks that ran from Walmart to Macy's to Kmart, etc. Each shop used a different "big store name". It was just meant to display a sense of humor.
I think that's exactly what you're looking at here.
