Quarrel was an English word used to describe an argument or disagreement. A quarrel involving two domestic partners was often called a lovers' quarrel. (TNG: "In Theory")
Craft used this word as an alias when he first met Zora aboard the USS Discovery, as it wasn't customary for an Alcorian to reveal their true name.
When she heard him say that his name was "Quarrel", she knew he was lying, and she immediately called him a "liar." (ST: "Calypso")