"Please be sure to specify THE name of THE section of the book you are commenting on." The reason for the definite article is that in a possessive phrase, the "owner" is most often treated as definite in English. That's why possessive phrases usually have the definite article or other definite elements like the, my, your, you, that, etc. Examples: THE 12th of May; YOU son of a bitch!; WE members of the board; YOUR day of reckoning; THAT way of thinking. In your example there are two possessive phrases containing OF: THE name of -and- THE section of.