How about "The UniCon Club"? sounds too much like a sci fi convention?

OK, perhaps a nod to the retro livery? "Blue Skyways Lounge"

Or, maybe the all-inclusive-merger-of-equals "Presidents Red Carpet Club" ?
(abbreviated PRCC by those "in-the-know")..

Or, why not offer bottle service and give it a trendy ultra-lounge moniker like "Blue"

the possibilities are endless.....