When referring to countable nouns, you should use a form like the following: Most men's names ... or Most of the men's names ... They mean essentially the same, however, you would probably use the second form when you are referring to a specific group of men. The first form is used when speaking about men in general (without a very specific group in mind). Use the 'most of' form when talking about uncountable nouns: Most of the cheese we eat is from France. Most of the water was wasted.

I'll have to give the proper sentence first. "Most men's names in the book (why did you leave that out?) begin with the letter A." We don't use "of" so much in this case. Only "most of them" or "most of the names" makes sense. Remember, "(they) begin" so you need a plural: names. You could equally say, "most male names..." You need "the" because you're being specific: "the letter which is A".