Hi,
Regardless of the specific reasons (discussed elsewhere at length), as we all know, QE2 had Queen Elizabeth 2 emblazoned on her bow. The use of the arabic 2 was highly unusual at the time.
The correct way to refer to the Monarch, is Queen Elizabeth the second / Queen Elizabeth II. On buildings named after her, you'll see it written correctly. Bridges, hospitals, roads, all sorts of things have been named after the Queen.
Therefore everything named after the monarch should be referred to a QEII not QE2.
Should we be correcting people who refer to these objects as QE2? I have been doing this, especially on twitter. I think it also serves to raise awareness of the ship.
The only thing in recent times I've seen that is just about OK to shorten to QE2, is when they talk of a second round of Quantitative Easing!