Cowboys seldom referred to their ropes as lassos. They usually just called them ropes, and the act of catching a steer was called roping. In the Southwest, the rope was also referred to as a lariat or riata, both from the Spanish “la reata”, again meaning rope.
At the end of the riata was a small reinforced loop, through which the other end of the rope would be passed to create a noose. This reinforced loop was called a honda.