It has to be the Jets. Every poll I've seen has Jets at 50% or better as the preference, with the other options (Falcons, Moose, Polar Bears etc) splitting up the other 50%. It's always been "Bring back the Jets", not "bring back an NHL team" - just not the same emotional attachment. Of course, it's not the same players after all this time. Same as the Bombers of today aren't the same as the 1990 Bombers. But they are still the Bombers.
And, finally, look at this from a PR perspective. There is a very loud, very vocal, very passionate "Jets" contingent. All other names, no matter how much they make sense, have no emotional attachment. Imagine, if you will, a public press conference being held at MTS centre, thousands of fans in attendance, awaiting the big unveiling of the new team name and logo. Hush falls over the crowd, fanfare, and the curtain is pulled off to review the new logo of "The Manitoba Falcons". Cue at least 1/4 to 1/2 of the crowd booing - for those fanatics, it's Jets or nothing. And they will boo. Even amidst the cheers of everyone else, you can bet that TSN will be showing the booing fans. PR disaster. Instant dissension and splitting the community. TV interviews with loudmouth fans who say "I wanted the Jets, I'm not buying tickets now".
Now, rewind. Same scenario. The curtain is pulled off for a brand new, updated logo for "Your Winnipeg Jets" screams the announcer. Loud, unified cheering, bedlam ensures, goes on for five minutes. PR heaven. TSN shows screaming, happy fans. Even those who are indifferent to the Jets name would still be willing to be behind this.
Sure, owners who pays for the team can choose any name they want. But it's the fan who pays for the tickets to keep the team afloat. And the majority want their Jets back. It will be the worst marketing disaster since "New Coke" if they don't come out as "The Winnipeg Jets." Guaranteed.
And about the whole "Manitoba" thing - don't be ridiculous. The team plays in Winnipeg. What, are we going to call them the "Manitoba-Northwestern Ontario-Saskatchewan-North Dakota Jets" just so the people in the geography feel attached? No, everyone will know this is Manitoba's team, they play in Winnipeg, and they are called the Jets. Naming them the Manitoba Jets won't bring anyone in from Brandon or Portage who wasn't prepared to come to a game in the first place. But around the world, the brand name "Winnipeg Jets" is still known. Winnipeg has been in popular culture in "The Simpsons" and "The Office". You name a sports franchise after the city, with the rare exception where it already works (e.g. Saskatchewan Roughriders).
You don't roll the dice on a name "you think" people will support, like the Polar Bears or Falcons or Manitoba Jets. You play the odds of knowing that at least 50% are passionate about "Winnipeg Jets" and you have an easier sell for the other 50%. You don't alienate a passionate Winnipeg Jets fan base who willl emotionally reject any other name.
Always my team, even at their worst.