It all depends on what Phoenix owns, do they own the rights to the name, or not? Probably not. Typically, if it's a product, the buyer wants the name above all else, due to recognition. If you're moving a sport team, and changing the name, the old name would have little value.
I'm sure that this issue was very, very carefully researched by the lawyers. It might be that the new owners wanted that name from the beginning, but didn't want to say anything until they had legal ownership cleared up.
That said, isn't 'Jets' a reasonable name for Winnipeg, because, if memory serves, there is/are companies in Winnipeg who specialize in jet maintenance? Bristol Aerospace comes to mind, along with the F18 scandal, but then again, my memory is cloudy. Moosehead, you know.
Furthermore, now that Winnipeg's AHL team has moved to St John's, NL, there's a Seadogs player who is going to play with them. Hope he makes it to the big leagues, there were 5 Seadogs drafted to the NHL last week.