The correct option is D women's
Let’s examine the sentence: “The ____ names are Helen and Lucy.” The sentence gives the names of two women and the blank would have the plural of woman, i.e women. This rules out Option A. Now, the sentence seeks to show that the names belong to women. So, ‘women’ should be used in possessive case. The possessive case shows ownership or belonging. With the addition of ’s (or sometimes just the apostrophe), a noun or pronoun can change from a simple person, place, or thing to a person, place, or thing that owns something. So, Option D has an apostrophe to show the possessive case and hence, that is the answer.