Officially, the new Winnipeg team regardless of name will inherit Atlanta's history. The Jets' history is part of the Coyotes franchise.
The only reason the Browns were able to keep the history in Cleveland, is that the NFL and city of Cleveland reached an agreement where the franchise would not be transferred to Baltimore, but the team would. What I mean is that the Ravens are technically an expansion team and the Browns simply went dark between 1996 and 1999.
Now you may see the new Winnipeg team do what the Washington Nationals have done and talk about Winnipeg hockey history. The Nationals' media guide always lists records as Washington, D.C. baseball history (both versions of the Washington Senators and the Washington Nationals) records for home runs and franchise (Montreal Expos/Washington Nationals) records for home runs.
As well, the new franchise could retire numbers for whomever they want. If they wanted to retire #33 for Patrick Roy, they could as it simply means they hang a banner and vow never to hand out that number again. My guess is you probably will see Thomas Steen and Dale Hawerchuk's numbers retired by the team, but that is irrespective of history.
Officially, I don't see the NHL rewriting history of the Jets, Coyotes, Thrashers and the new Winnipeg team. The Jets' history will be linked with that franchise and thus will keep with Phoenix (and whereever they may end up). As well, Atlanta's history will be kept with that franchise and end up in Winnipeg. The Thrashers did not pick up the history of the Flames time in Atlanta.
If history is to be honoured, if the new Winnipeg franchise calls themselves the Jets, won't they need a new logo? Seems to me at that final salute in 1996, the team retired the logo too. So if history is to be honoured, a new logo is mandatory.
This does bring up an interesting question somewhat related to this. What is the situation in Hartford? I know the City of Hartford owns the Whalers name and logo, do they also own the history of the Whalers or did Carolina take that with them?