"Tess of the D'Urbervilles" is the name of the heroine – sort of. There's a lot of discussion about what Tess should be called, and the change in her last name from the common-sounding "Durbeyfield" to its nobler original, "D'Urberville," is what sets the tragedy in motion. Tess is a common, country girl. So to call her "Tess of the D'Urbervilles," as though she were a great aristocratic lady, is ironic and tongue-in-cheek. For more about the name "D'Urberville," see the "Character Clues" section.
The subtitle of the novel could use some more attention, too. "A Pure Woman" wasn't part of the title in the novel's original manuscript, or in its initial publication in the Graphic magazine. But before the Graphic magazine agreed to publish it, Hardy was hurt by criticisms from various publishers who refused to print it in their magazines on the grounds that it was immoral. One publisher, for example, criticized it for its "frequent and detailed reference to immoral situations" (i.e., Tess's rape by Alec, Tess's sexual attractiveness). Another publisher put it more mildly: "the general impression left on me by reading your story […] is one of rather too much succulence" (You can read more of the publishers' objections in the "History of the Text" section of the 1998 Penguin edition).
As Hardy was revising the novel for its publication as a single volume in 1891, he felt the need to defend his heroine and her inherent purity – so his addition of the subtitle, "A Pure Woman" can be read with a tone of defiance. He's insisting that Tess is "pure" despite the fact that she has a child out of wedlock. She's still the moral center of the novel. Hardy refers to this as "paradoxical morality."