The eponymous character in The Merchant of Venice is Antonio, not the more well-known Shylock, or the protagonist Bassanio (who is a student). This is made explicit by the front cover of the 1600 quarto: The moſt excellent Hiſtorie of the Merchant of Venice. VVith the extreame crueltie of Shylocke the Iewe towards the ſayd Merchant, in cutting a iuſt pound of his fleſh: and the obtayning of Portia by the choyſe of three cheſts.
The song "In the Hall of the Mountain King," the most famous piece in the incidental music Grieg wrote for the play Peer Gynt, is often simply called "Peer Gynt". "The Mountain King" referred to in the title of the song is not Peer Gynt, the protagonist of the play, but an evil Troll.
In the UK it's most commonly known as "the Alton Towers theme", Alton Towers being a theme park that plays that piece in its advertisements as well as around the park itself. However that's probably another trope.
The extremely famous opening chorus "O Fortuna," from a certain cantata by Carl Orff, is often referred to as "Carmina Burana", ignoring the rest of the work. And only the people who read right through the liner notes know that "Carmina Burana" (Songs of Beuern/Benediktbeuern) should actually refer to the whole body of Latin and German poetry found in the Benedictine abbey at Benediktbeuern when it was dissolved, and not just the handful that Orff set to music.
The Barber of Seville subverts this. As most people would guess, Figaro is the barber, but Almaviva is the protagonist.
The leading tenor character in Pagliacci is not named Pagliacci. His real name is Canio and the clown character he plays is named Pagliaccio("clown"). "Pagliacci" is the plural of "pagliaccio," meaning "clowns," and refers to all the principle characters.
The song from Offenbach's Orpheus in the Underworld commonly known as "The Can Can", after the dance performed to it, is actually titled "Infernal Galop".
Fiddler on the Roof: The protagonist Tevye the milkman neither plays the violin nor stands on a roof. The Fiddler is a separate walk-on character with very few appearances and no spoken lines. (He functions as a metaphor for the show's theme of balancing tradition and modernity and the situation of the Jews in the country.)