In the time of William Shakespeare it was a perfectly socially acceptable to refer to people by their race or ethnicity. That is how the play Othello came by its subtitle, ''The Moor of Venice.''
The term ''Moor'' has been used historically to refer to people who are Muslim, African, Arab, or just generally not white or not Christian. While it can mean many things, it's certain that the term is racially and culturally charged, and not in a flattering way. Othello, being not white, would therefore be even more likely to be singled out as the Moor of Venice. There probably weren't a lot of nonwhite people to choose from, so he was most likely quite noticeable. This would have contributed to his status as an ''other.''
The term ''other'' is used here in the sense of one who is set apart from the cultural mainstream. It brings with it connotations of discrimination and of being valued as less than one who is not an other. It can also be used in verb form: the act of othering is the act of making someone an other, which is precisely what happens to Othello.
Shakespeare himself sets Othello apart as an Other in adding ''The Moor of Venice'' to the title of the play. The characters follow suit and perpetuate that ''otherness'' throughout the play.
Additionally, the repetition of the "Moor" is Shakespeare's way of showing racism. In the play, Othello is called "Moor" more often than "Othello"; Moor is his identity. Roderigo, Iago and Brabantio all find Othello's racial backround, especially since he married a white woman, very undesirable. When Iago is talking to Brabantio with Roderigo about Othello and Desdemona's marriage, he said: "Even now, very now, an old black ram is tupping your white ewe." Brabantio - The senator - gets angry when he finds out that his daughter, Desdemona, has been seeing "the moor" behind his back and he makes racist comments about Othello to his face. He accuses him of witchcraft because he couldn't believe that Desdemona would ever "fall in love with what she feared to look on," and he suggests that Othello's race makes him capable of these powers of "black" magic.