Thus, I don't expect a renamed Coyotes team until 25/26 season. Need time for the trademarks, unless Smith has already done that. As it sounds like these chats with the NHL began earlier this year, but still, it's important for pro sports teams to secure their trademarks.
I'm not an IP lawyer, but it doesn't take anywhere near that long.
tmsearch.uspto.gov
Boom - there's your search.
Searching Utah Yeti comes back with 1,183 hits - but the first couple dozen are mostly different variations from Yeti Coolers - but there are other hits as well. Because "Yeti" is an actual word, Yeti Coolers isn't able to own the rights to the entire word (just like tech giant Apple doesn't own the word "Apple".
Now a couple hits do come up under "Yeti Hockey" - but they've been abandoned as of 2021.
So what would happen: you make your searches. You, along with your attorney, decide that it is extremely unlikely your trademark application for Utah Yetis will be rejected. So you make your application. USPTO analyzes the application, other people might challenge it, and eventually you receive your registered trademark (unless if your attorney is a buffoon).
But that's just for a registered trademark. You can proceed with an unregistered trademark - and you can even still fight people infringing on your unregistered trademark.