It's something I could see sticking in the future. Like a small part of it at least. Regular division names stick, but the official logo for the divisions end up having the sponsor logo on them.
Speaking of which, I wonder if that could lead to NHL wanting MORE divisions. The plan when Seattle enters is 4 divisions of 8 teams. But if NHL wants to have the sponsors for divisions, what if they do 8 divisions of 4? That's double the amount of division sponsors you can have, while having more intense rivalries between closely located teams, and the playoff format ends up being the 4 division winners plus the next 4 best teams.