Stanza 3 Summary

Get out the microscope, because we’re going through this poem line-by-line.

They name thee before me,
A knell to mine ear;

As with the second stanza, the third picks up right where the second left off (this pattern will continue throughout the poem). It gives it a nice figure, don't you think?
Apparently some mysterious "they" names the woman before the speaker. In other words, various other aristocrats and elites talk about the woman in front of him. They gossip, as it were.
Whenever this happens, it's like a "knell" to the speaker's ear. A knell? Yeah, a knell. You know, that word meaning the sound of a bell.
But it's not just any old bell. Usually, a "knell" refers to the somber, slow, sound of a bell being rung to announce a death, the so-called "death knell."
This word is never really a good word. Thomas Gray, for example, talks of how the "curfew tolls the knell of parting day."
The point is, even the mention of the lady's name in front of the speaker is painful. Remember, he and she have said their goodbyes, and he is none too happy about it.
The name itself sounds like a death knell for our speaker, which here is a metaphor for how even the uttering of the woman's name makes the speaker think of death—the ultimate departure or end.

A shudder comes o'er me—
Why wert thou so dear?

The speaker elaborates on what happens to him when he hears her name mentioned: a shudder comes over him. He feels about the same way you do when you look at these things.
Thinking about all this departure and death knell business prompts our very unhappy speaker to ask an interesting question: "Why were thou so dear?" Why did he ever care for this beloved at all, when now he's all oogied out at the mere sound of her name?
Anyway, the word "dear" here means "special" or "super-important." You might say that your iPhone, or your kitten, is very "dear" to you.
Ironically, the speaker realizes that the woman was really dear to him because even hearing her name makes him think really bad, unpleasant thoughts.

They know not I knew thee,
Who knew thee too well—

Now it seems like while he's at these aristocratic parties, sipping tea with this pinky finger in the air, the speaker has a dirty little secret that nobody else knows: he "knew" the woman they speak of. And he didn't just know her, he knew her "too well."
Yes, that "who knew thee too well" describes the "I" of line 21. You could rearrange it like this: "They don't know that I used to know you, used to know you too well in fact." Of course, that's not as cool-sounding.
It's not often that we get to say this, but "knew" here doesn't just mean "familiar," as in, like, a normal, platonic sense. Oh, no no no.
"Know" here is probably intended in the biblical sense as well, where it means "to have sex or relations with." Don't believe us? Check out Love Potion, errr definition, number 9.
The speaker is saying he too has been sexually involved with this woman (hence the shame), perhaps too sexually involved.

Long, long shall I rue thee,
Too deeply to tell.

Because he has had to part from her, because she's now with another guy, because he "knew" her too well—because of all this, the speaker will "rue" the woman for a long, long time. He will "rue" so deeply, in fact, that it can't be explained ("too deeply to tell").
"Rue" here is not the French word for a street (as in Poe's story "Murders in the Rue Morgue"), but a verb that means to feel sorrow, or regret. It's like wishing something had never, ever… ever happened. (Next time your bro thinks of stealing your Katy Perry album say this: "You will rue the day you chose to steal it." That should teach 'em.)
The speaker is sad about his relationship with the woman, but in a very specific kind of way. It's not just sadness, but also a form of regret.
It's hard to tell just where this regret comes from. Does he rue the fact that he had sex with a married woman? Is he upset that he even got involved because now it's making him really sad?
We really have no idea what the speaker's real issue is. We know he's upset, and that he misses the girl, but we're guessing there's a lot more going on than is obvious on the surface of these lines.