You've probably heard people call this book by two different names: "Song of Songs" and "Song of Solomon." Seems like a pretty big difference—what with the addition of a King's name and all—so what gives?
The first line of the book, directly translated, is "The Song of Songs, which is Solomon's" (1:1). So there you have it.
But what's the deal with Solomon? Is he the author? Is he the groom? Or is the book just dedicated to him?
Check out our "Figure Analysis" on Solomon for more, but our educated guess is that it's just a dedication. Often, ancient writers (or later editors) would dedicate their work to a noble patron or even to a cultural figure. It basically just upped your street cred.
P.S. You might hear people refer to the book as the "Canticles." That comes from the Latin version of the words Song of Songs (Canticum Canticorum). Just a little dinner party trivia for you.