The comet that Maria (pronounced mah-RYE-uh) Mitchell discovered was designated C/1847 T1. But it has popularly been known as "Miss Mitchell's Comet". She received a gold medal from the King of Denmark for the discovery. The first discoverer of a comet that could only be seen through a telescope was eligible for this prize at that time.
The very first woman to be credited with the discovery of a comet was
Caroline Herschel in 1786. Hers got the popular nickname of "the first lady's comet". She went on to discover another seven, so if the Danish king of her time had been so generous, she'd have had quite a collection of medals!
Although Miss Mitchell never met Miss Herschel, a few decades later, she traveled to Britain. She was warmly received by Caroline Herschel's nephew, Sir John Herschel, and his family.