Who named the first comet?

Edmund Halley was one of the earliest astronomers to recognize that comets - some comets, at least - are periodic, and return to the inner solar system with predictable periods. French astronomer Nicolas Louis de Lacaille was the first to propose the name "Halley's Comet" in his honor, after Halley's prediction had been borne out by the comet's reappearance on schedule.

However, people had been naming comets for centuries before, as "the comet of <year>".