The "Tribal" namesakes were specifically rejected for use on the CSC program due to the wide variety of issues that comes with trying to encompass such a diverse and historically sensitive into a comprehensive class. If we didn't use them on largest and most capable surface combatant class in the history of the RCN, the submarines will similarly miss such an opportunity as well.
Regarding naming the CPSP, there is some historical precedent to look at.
All of the submarines from WWI through to WWII were numerical and alphabetical combinations, not really suitable for our modern sensibilities. Our Oberon class (Ojibwa, Okanagan & Onondaga) all have indigenous names which we've established is likely a no go. We had a pair of US loaned submarines (Rainbow and Grilse) throughout the 60's and 70's, which I think is one of the best options regarding a namesake for the CPSP.
HMCS Rainbow was the second warship Canada ever commissioned in its history, so it is a vessel worthy of being the class namesake. I am partial to the theme of naming vessels after fish, likely from across Canada if they use that. There is countless possible options, so I'll leave it to the imagination of folks to pick some appropriate sounding options. There is some potentially great names (Steelhead, Sockeye, Pike, etc) but quite a few options.
There was many, many different naming schemes floated for the Victoria class before they threw up their hands and named yet another class of ships after towns/cities. Explorers, ports, battles, bodies of water/watersheds, marine mammals/fish, indigenous leaders, etc.