The NHL has its 4 conferences, and with Seattle joining a team is likely to have to swap - presumably Arizona to the central.
Now what I suggest is that this is as good of a time as any as entirely remaking the conference/division system
Here's a link to one idea
https://i.imgur.com/eJElS2S.png
Another one is rotating Stl/Nashville to green, Seattle/Vancouver to red, Toronto/Buffalo to blue and Chicago/Detroit to yellow - or something like that.
There could also be smaller divisions of 4, noted in black, rotating which other divisions they play, but obviously prioritizing the closer ones for convenience in travel time etc.
Now some of the rivalries would change, but in the long run the best way to go about it is probably to minimize distance between the teams playing each other more often.
I renamed all the divisions, and felt personally that "south-west" etc would be very boring names, so I took myself some creative liberty. I'm not American myself, so if you have other suggestions for division names, please comment!
Here are the All-Star teams for each division, consisting of min 2 players from each team, mostly based on last year.
Starting with the yellow area, south-east, or Appalachian as I named it.