Did Tess finally know that Alec was not a d'Urberville?

Question

I have watched two film adaptations of Thomas Hardy's Tess of the d'Urbervilles, in both of which Tess was made aware that Alec was not a true d'Urberville, but his family simply adopted the name. I've already read the novel but I can't remember if Tess was actually informed about this in the novel. If yes, please give me the page number.

Answer 1

At least by implication, yes.

Twice, in conversation with Tess, Alec refers to himself as a "sham" d'Urberville:

“If you are a genuine d’Urberville I ought not to tell you either, I suppose. As for me, I’m a sham one, so it doesn’t matter. It is rather dismal. It is that this sound of a non-existent coach can only be heard by one of d’Urberville blood, and it is held to be of ill-omen to the one who hears it. It has to do with a murder, committed by one of the family, centuries ago.”

_{-- Chapter 51}

He stamped with his heel heavily on the floor; whereupon there arose a hollow echo from below.

“That shook them a bit, I’ll warrant!” he continued. “And you thought I was the mere stone reproduction of one of them. But no. The old order changeth. The little finger of the sham d’Urberville can do more for you than the whole dynasty of the real underneath.... Now command me. What shall I do?”

_{-- Chapter 52}

Earlier, Tess tells Alec that she "undeceived" her father of the notion that they were related. Since Tess and her father know that they are descended from the "true" d'Urbervilles, this means that certainly Alec can't be.

“If your mother does not recover, somebody ought to do something for them; since your father will not be able to do much, I suppose?”

“He can with my assistance. He must!”

“And with mine.”

“No, sir!”

“How damned foolish this is!” burst out d’Urberville. “Why, he thinks we are the same family; and will be quite satisfied!”

“He don’t. I’ve undeceived him.”

“The more fool you!”

_{-- Chapter 50}

The following, from much earlier, is less conclusive, as the knowledge of Alec's family being sham d'Urbervilles could be interpreted as that of an omniscient narrator rather than Tess herself, but it does seem to be written from her point of view:

How stupid he must think her! In an access of hunger for his good opinion she bethought herself of what she had latterly endeavoured to forget, so unpleasant had been its issues—the identity of her family with that of the knightly d’Urbervilles. Barren attribute as it was, disastrous as its discovery had been in many ways to her, perhaps Mr Clare, as a gentleman and a student of history, would respect her sufficiently to forget her childish conduct with the lords and ladies if he knew that those Purbeck-marble and alabaster people in Kingsbere Church really represented her own lineal forefathers; that she was no spurious d’Urberville, compounded of money and ambition like those at Trantridge, but true d’Urberville to the bone.

_{-- Chapter 19 (emphasis mine)}