The video starts with Clarkson saying: "It's been months, we still have no name."
The men then start offering suggestions, but get nowhere fast.
Hammond suggests "Automates", only for May to reply with a resounding "No".
Hammond then offers up "Tripod" and again May quickly shoots him down, this time by saying: "That's someone with an erection".
Clarkson gives his two cents, and both turn out to be associated with English rock band Genesis - "Selling England by the Pound", "Watcher of the Skies".
So Hammond steps up and, in true Top Gear fashion, asks Clarkson sarcastically: "Are these just album titles?"
Clarkson then pretends to be serious and begins one of his monologues.
"The show, I think, will sit on the internet like - and this is what I'm suggesting for the name - a small puddle of excellence."
The video, which runs for 1.29 minutes and features more ridiculous name suggestions, ends with the hashtag: #TheStillVeryMuchUntitledClarksonHammondMayAmazonPrimeShowComingAutumn2016.
The wait continues.