When we say "I Am," we're pretty much saying we're alive or we exist. That's the point of this title, although it is a little weird (we'll get to that in a sec). The speaker's friends no longer care about him; it's almost like he's dead. He feels like a ghostly vapor, and is surrounded by the shipwreck of everything he once loved. But—dude isn't dead! He's still very much alive, and still has feelings. That's the point of saying "I Am." The speaker doesn't want people to abandon him or treat him like he's dead yet because he's not.
The other thing about the title is that we feel there should be something after the "am." If somebody says "I am," our next question is usually "Okay, you are what, bro?" Well, the speaker is a lot of things. He is the "self-consumer" of his "woes" (3), he is sad, he is "like a memory lost" (2), he's like "vapours" (6). The point is the speaker is a lot of things, so the title is sort of like a placeholder. Clare couldn't have called it "I am x, I am y, I am z," after all. By just naming it "I Am," he invites us to question his identity further and learn more about him. He piques our curiosity.