My guess is that the renaming will be July 1. or on the first day of the next NHL season. They will not change the name during the playoffs.
My guess is some varriant like NBC Sports Channel, NBC Sports Network, or NBC Sportsnet. "SNBC" is already take by Shop NBC, and is already confusable with MSNBC. However with Microsoft no longer a partner in the news/comment channel, and Comcast seemingly eager to distance itself from the past excesses of that crew, we might see NBC Sports Channel (Versus), NBC News Channel (MSNBC), NBC Business Channel (CNBC, which loses access to WSJ material next year to Fox Business Channel), and maybe even NBC Golf Channel, and NBC Entertainment Channel (USA).
I think that the new management is serious about competing with ESPN. A sports news played more seriously and with less basketball than SportsCenter, and serious competition for rights to other events rights, would go a long way.