From what I can tell, there has been absolutely nothing to ever suggest Qatar Airways would be a sponsor other than fan speculation alongside Toyota and Bank of America.
Wouldn't exactly roll off the tongue like The Lexus or The Megafon would.

Everton mailbag: Moyes’ summer plans, stadium naming rights, pre-season in the U.S.
The Athletic asked for your Everton questions - and they piled in. Patrick Boyland attempts to provide the answers...

Best I can get you