While I can't suggest any tag team names off the top of my head that I genuinely think would involve themselves with such a tournament, I do think that a tag team tournament would be a very fun idea. Having annual tournaments rotating around different themes every three or four years is a great way to invite and exploit new and exciting talent from across the world, and opens up new gateways for talent to be recognised on a grand scale (via the Network) and so introduces them to probably many unknowing members of the WWE Universe. The cruiserweight tournament and women's tournament have been great successes and have / are going to open up many doors for new talent to come through. And knowing how weak the tag team scene can get in the WWE at times, I think a tournament like this could definitely work.
Though, I do question whether there is such a demand for a tag team tournament. There had been a clamouring for years about bringing back a focussed cruiserweight scene to WWE, and women's wrestling is surely at an international peak right now, so those tournaments make sense. There are definitely tonnes of great teams out there, but are fans interested in a tag team tournament? I don't know the answer, which is why I pose the question. It's a different question to whether there will be a tournament. I personally enjoy tag team wrestling, but it is no longer what it once was in the prominent western wrestling companies. Perhaps that's the problem and actually a tournament would be worth it's while. I'd like to see a tournament like this and I think it naturally makes sense, but I question the demand when there could be different specials that WWE focus on instead.