Luffy is his name. Monkey D. Luffy (last names first in this world, however, interestingly enough, it doesn't seem as though everyone has a last name. Hm. I just noticed that). Straw Hat is the epitaph given to him by the marines because of the straw hat he always wears.
Oh goodness no. He's barely a teenager and I'm in my late twenties. Many things I am, Isabela, a cougar is not one of them. However, he did save my life, so I am rather fond of him.