Though an earnest effort is underway on Twitter to rename the Atlanta Thrashers in the event of a highly likely move to Winnipeg, it looks like the club won't be able to go by the name Winnipeg Jets once they (likely) arrive. That name is still owned by the NHL.
According to the renowned Chris Creamer of SportsLogos.net fame (and quite a few others), the Thrashers are much more likely to become the Manitoba Moose. That name belongs to the American Hockey League squad that currently inhabits Winnipeg's MTS Centre, the rink at which the reformed Thrashers would play.
If that happens, then Atlanta can claim a small technicality victory in one very specific regard. How many times have we been told that the Winnipeg Jets are returning to their original home? Ha! You did not get back your Winnipeg Jets! Atlanta wins at hockey!