If you mean the person, you say "Queen Elizabeth the Second".
If you mean the ship, you say "the QE2", or "the Queen Elizabeth the Second". Note the definite article.
2015年8月31日
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Yes, Queen Elizabeth the second, unless you're talking about the ship when most people say 'the QE2'.
2015年8月31日
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That's right. This distinguishes her from QE the First [although she lived many years ago]