The play is called "The Tragedy of Othello, the Moor of Venice": the title joins the protagonist's name, the label of Moor, and the city he serves as general. Within the play, several characters call him Moor, sometimes with contempt, sometimes with respect.
Iago makes the label a mockery already in the first scene: he says he will be "only the ensign of Your Moorship!". Brabantio uses it to accuse, saying that Othello bewitched his daughter and that she would not trade her guardian for the "dark breast" of a thing like him. In the Senate, however, a senator receives him as "the valiant Moor". And Othello himself, in Act III, Scene 3, lists among the reasons his wife might have left him: "Perhaps because I am black".
The part "of Venice" says whom he serves. In Act I, Scene 3, the Duke summons him at night because he needs him against the Turks: "Brave Othello, we must use him at once". In the end, it is Venice, through Lodovico, that takes his command and hands it to Cassio. Iago tells Roderigo, in Act IV, Scene 2, that Othello, if replaced by Cassio, would sail "for Mauritania".
The title thus joins the man and the label, the general that Venice employs and whom others call Moor. At the end, when Lodovico asks about "this unfortunate, reckless man", Othello answers: "He that was Othello? Here I am."