The original title of this poem wasn’t "The Love Song of J. Alfred Prufrock." It was – ready for this? – "Prufrock Among the Women." We’re glad Eliot changed his mind about this original title, which sounds like a terrible 1950’s musical. But it does tell us that Eliot thinks Prufrock’s relation to the fairer sex is at the center of this poem. "Love Song" makes a similar point, but not as directly.
The title is actually the only place where Prufrock’s name is mentioned – in the poem he talks about himself in the first person. Eliot is clearly poking fun of himself with this title – as a young man he signed his name "T. Stearns Eliot," but that doesn’t mean the poem is biographical. For one thing, we’re pretty sure Eliot didn’t drown in the ocean. The other thing to know about the title is that it’s completely ironic in light of the poem, which is not so much a "love song" as the depressed ramblings of a lonely and cowardly man. If you have ever seen The Daily Show or one of the other "fake news" programs, then you know the kind of irony that’s at work here. The title of the poem is only pretending to be serious, while the poem itself is more like a "fake love song."