Seattle Eagles, Seattle Rainiers, and Seattle Whales just sound awkward.
Renegades sounds minor league and says nothing about Seattle.
Cougars is fine, but unoriginal even within the NHL itself. Likewise, Seals has been done already and it would be a little disrespectful to the memory of that team.
“Totems” is a nice reference but makes no sense as a group identity.
Kraken is awesome at one level, but I really think the era of singular names has come and gone at this point.
Emeralds and Evergreens are both above the Mendoza line for me, but I think it would be extremely challenging to come up with a proper logo to express either of them. It could be pulled off, but I wouldn’t count on it.
That leaves: Firebirds, Sea Lions, Sockeye
Of the three, I think Sockeye has the most upside to be something different and fun, but not stuck in an era. It gives the franchise room to be young and creative, but also with an obvious angle for adding an aggressive edge. I can imagine Seattle Sockeye merch having a cult audience of non-hockey fans, sort of like Whalers gear but without relying on the retro/hipster appeal. The other two would be easy to do “pretty well” with, but Sockeye could potentially be one of the best identities in the Big 4.