Now, here is a question:
Why is the current operating ship named "Queen Elizabeth" not named "Queen Elizabeth 3" ?
Otherwise, and as stated above, the use of the Arabic "2" was appropriate and not the Roman "II". The Queen did get it wrong. As to the use of "QE2", I never had a problem with it from a marketing standpoint, and some of the early logos were quite nice. Using "QEII" might have some pronouncing it as a word, perhaps "Q-eye"? Cunard had to move forward from the old days, and the use of QE2 certainly worked; it just flows off the tongue.
There's Queen Mary (Long Beach, CA) and Queen Mary 2. Anyone remember the story (I never felt it was proven) as to the naming of Queen Mary? She was supposed to be Queen Victoria. Of course that has been taken care of with a Cunard "cruise ship" of the same name (she was actually first intended for Holland America).
Then again, Holland America Line has named six ships "Rotterdam" without any number!
Not much consistency in naming, but at this stage it means very little.