True North Sports and Entertainment is in the midst of their Drive to 13,000 season tickets, and according to CBC News, they won't announce a team name until that campaign is over. Scott Brown of TNSE said that the company doesn't want to get people ahead of the curve, and that they want the focus to remain on the all-important ticket drive.
If the goal of 13,000 season ticket sold isn't met, it's possible the NHL's Board of Governors could deny the request to relocate the Atlanta Thrashers to Winnipeg. It's highly unlikely that happens, though.
The campaign will have to end by June 21 at the latest, when the BoG meets to vote on the relocation proposal. Likely, it will end before that, but that's dependent on when the 13,000 goal is met. It could be a day after tickets go on sale to the general public on Saturday, or it could be a week or two after.
In any event, you have to assume the team name is known by folks inside TNSE. If they have to wait until June 21, for example, they'd have less than a week to create their new identity before the NHL Draft, when they presumably will parade out a new look when they make the No. 7 overall selection.