Can’t you ask the same question next year? If the team is “Utah Yeti” singular you can’t really say a player is a Utah Yeti, you would have to say he is a “member of/player for the Utah Yeti”. Same as Lightning, Wild, Kraken, etc.
Well, I
think he could be a Yeti, Kraken, Lighning, or a Wild. But what he couldn't really be is a Hockey Club. As you said, he would have to be a "member" of the Utah Hockey Club. The problem with "club" is that it is singular but defined, in part, as a group.
I can't believe I am going down this rabbit hole. If I work for Shifting Sands Engineers, I am an engineer. If I am in Congress, I am not a Congress. I am a member or Congress. I might even be an inmate, but that is a different story.
I got bored and looked up the plural of kraken, and Merriam Webster listed both krakens and kraken as the plural. Yeti appears to be singular, so yetis is the only plural I could find. For those into this stuff, the reason the plural for kraken does not need a trailing "s" is that it is a Norwegian word, and foreign words apparently often become plural without an s.
Now my head hurts!