I am all for tradition, we call our ships HMCS (Her Majesty's Canadian Ship).
Officers hold a commission from Queen Elizabeth.
The Army has the RCD, RCR, 22eR, plus all the reserve units with "Royal" in their names.
I don't think I would like to sail on a ship called CSS Halifax or whatever, just doesn't sound right.
I don't see it happening though, just the cost of changing the infrastructure, letterhead and everything else that goes with it.
My 2 cents for what it's worth.