The poem "Richard Cory" is all about a dude named—that's right, you guessed it—"Richard Cory." The poem describes his good looks, his money, and ultimately his suicide. Without Richard Cory, "Richard Cory" would be, well, pretty much two lines about the townspeople.
Given all this, the title's pretty much a no-brainer. Not only does it announce the subject of the poem to come, but it also sets a focal point for us readers, just like how R.C. is the focus of all the down-towners in the poem who look up to him with envy and admiration.