No, and No.
While re-naming a specific town / physical feature can make sense in the most offensive of situations, it has now become a Politically Correct Fad that is just as insulting / indifferent to history as it is trying to be apologetic.
Example, the Salish Sea made sense. 2 reasons, It was largely the Salish people who lived in the area AND the current post colonial names are still official too. This is because the name, "Salish Sea" did not replace "Georgia Straight," but instead refers to the greater combined area of the "Georgia Straight," "Juan de Fuca Straight," "Howe Sound," etc... It actually annoys me how many people get this wrong.
Re-naming the entire province of BC would do nothing but split people apart and create animosity within the province.'
Also, my biggest point is that before post colonialism the province of BC did not exist! There was no single native group / culture that inhabited the exact (or even rough) borders of the province. It is a geographic entity that was created afterwards and encompasses the new modern day reality of the land, politically and socially.
Many towns and regions within BC do have native names honoring the native ancestry of the province (Kelowna, Kamloops, Cariboo, Chilliwack, Comox, Coquitlam, Kitimat, Lytton, Lillooet, Malahat, Nanaimo, Okanagan, Penticton, Saanich, Sechelt, Squamish, Sumas, Tsawwassen, and Yoho just to name a few of the top of my head! So honestly, there is no lack of cities, towns, regions, parks, etc... that have native names in BC.
Like it or not, but North America was a ticking time bomb of eventual colonization, either from Europe or Asia, it was inevitable that one of these massive regions with exploding populations and far superior / industrializing technologies was going to "discover" the Americas and colonize them. Many people treat it as the only time such a thing had happened, but truth is this was an ongoing cycle of empirical conquest that had been going on for millennia before in both the old world and the new world.
Today, BC is far more than just native land / ancestry, and I think it is important that it retains its wide variety of name cultures (Native, English, Spanish, Italian, French, etc...) to also honor / remember how it became the entity it is today. If anything a few select places should be appropriately renamed with East Asian / South Asian names.
The name British Columbia also reflects how, unlike the rest of western Canada, our province (similar to the Maritimes) had its own pattern of settlement from the coast into the interior.
And what is there not to love about the BC flag? It represents the sea, the mountains, and the setting sun. Wonderful. Maybe they want to add some native art elements to it, but while if done appropriately it could look nice, it also runs the risk of coming off "desperate" and cheesy.
This really feels like an "if it isn't broke, don't fix it" moment. But I guess life has become so stable and good in our evil post-colonial hell hole
that we can now debate such trivial matters.