Well, as far as the idea of modesty and shocked locals goes, if you stay at a fancier or more Westernized hotel, there won't be any real problems in the hotel itself. Outside of the hotel, and especially outside of the tourist zone, though... If you look similar to her, call yourself her brother and hold off on PDA until you are in your rooms. (General rule about the Middle East, actually) Or you can call yourself her fiance, that sounds more respectable. Or get two rooms and only use one, so that everyone can appreciate that you at least attempted to respect local customs without ruining your holiday by separating during the duration. Sorry if this isn't too helpful or specific, I've never gone traveling with a significant other so I don't know the specific details about that. about 4 years ago
Technically - no.
Reality - yes. Lots and lots of people holiday in the UAE and are not married. As long as you are respectful and don't attract attention to yourselves, then you will be fine. It is very common here for husbands and wives to have different surnames as women do not change their name when they get married, so no one will notice or comment on this.
You are better off staying in one of the bigger 4/5* hotels as they wont comment. almost 4 years ago