question about switching my S6 to another carrier

[marklyn]

I'm moving my SM-920V from Verizon to Tmobile. My baseband version is currently specific to Verizon so when I switch will my future firmware updates be coming from Tmobile and will the baseband version change to reflect Tmobile?
I guess what I'm confused about is if I were to manually download and install a future firmware would I be looking for one that is Tmobile branded for my phone?