Why might Eliot have called this a "love song"? If you were titling it, would you keep "love song" or use some other phrase?

We find the phrase "love song" in the title of the poem for a few reasons.

As a description of the speaker's sad, lonely wanderings and failures to connect with women, "love song" is a fairly accurate and straightforward description: the speaker yearns for love and intimacy without receiving it. Think of how many actual love songs you know that are about unrequited love, or failed relationships! They're very common.

And, paradoxically, "love song"...

We find the phrase "love song" in the title of the poem for a few reasons.

As a description of the speaker's sad, lonely wanderings and failures to connect with women, "love song" is a fairly accurate and straightforward description: the speaker yearns for love and intimacy without receiving it. Think of how many actual love songs you know that are about unrequited love, or failed relationships! They're very common.

And, paradoxically, "love song" works as an ironic description of the speaker's struggles, too. He doesn't find love, and he's too much of a coward to even try very hard to find it, and so he's definitely not singing a love song to any lady in real life!

To sum this up so far, although it sounds crazy, the poem both is and is not a love song, so the phrase "love song" in the title is both straightforwardly appropriate as well as ironic. But here's my favorite guess about why Eliot titled the poem with that phrase: "love song" also works to make the title funny. We might expect a poem to be called, for example, "The Love Song of Romeo" or "The Love Song of James Smith" or any other normal-sounding name. But this is "The Love Song of J. Alfred Prufrock," which is hilarious when you think of how stuffy that name really sounds. It's like saying "The Love Song of F. Humphrey Q. Longwhiskers III." I'm exaggerating, but you get the idea: the man's name is awkward and snobby, so putting it next to the phrase "love song" is funny.

For all those reasons, no, I, personally, wouldn't change the title of the poem to something else. It works too well as it is. But if you were interested in creating a more straightforward title, you might pick something like "Lonely Wanderings," or you might just echo a line you particularly like that embodies the theme, like "Ragged Claws" or "Indecisions" or "Music From a Farther Room."

You might be interested to know that Eliot himself originally titled this poem "Prufrock Among the Women" (according to the book T.S. Eliot: A Life by Peter Ackroyd). So if you were looking for a more appropriate title that expresses the fact that Prufrock wanders around among the women without actually wooing them or connecting with them in any meaningful way, that title would do the job.