Disney kind of did it wrong. When picking a name for a sea-witch, a name that means "little she-bear" seems a bit ridiculous for a character that lives underwater.
Like the constellations Ursa Major and Ursa Minor, which mean "she-bear," these are the feminine Latin diminutives of Ursus, "bear." Both Ursa Major and Ursa minor have unique stories from several different cultures. Ursula (Ursa too) is a girl's name most do not consider using today, but one that is rich with history and culture.
Saint Ursula of the 4th century was a virgin princess of Britain whose popularity during the Middle Ages may have increased the name's usage. Her [now accepted as fictional] tale says that she sailed with 11,000 virgin handmaidens to meet her future husband, but when a storm brought them to their destination in just a day she decided to on a pilgrimage around Europe with the pope and bishop. They soon arrived in Cologne, all 11,003 of them, where the town was being raided by Huns. I. The end all of the virgins were killed, Ursula specifically being shot with an arrow. It is unclear what happened to the pope and bishop. Saint Ursula has been a very popular subject of paintings throughout history. A little known fact is that Christopher Columbus named the Virgin Islands after Saint Ursula and her handmaidens, and later Ferdinand Magellan named Cape Vigenes after the virgins.
Saint Ursula Ledochowska came later. Born in Austria to a Count and Countess, her birth name was Julia Maria. She founded the Congregation of the Ursulines of the Agonizing Heart of Jesus. Two of her other accomplishments were starting an orphanage, and starting a home for female university students.
Author Ursula K. Le Guin is known for her fantasy novels, one of which - Tales From Earthsea, was made into an animated film by Studio Ghibli.
Actress Ursula Andress was a gorgeous Swiss-American 60's movie star known for her roles in "Dr. No," "Casino Royale," and later in 1981 she was in "Clash of the Titans." A few other actresses have been named Ursula.
Ursa was also one of the bad guys in Superman II, but in the newer versions her name is Faora. In Shakespeare's Much Ado About Nothing there was a character named Ursula. Ursula has also been a name used by Honore de Balzac, J. K. Rowling, Sheila Lavelle, and a few TV shows and other stories.
Ursula has several variant forms, including Orsola, Orsolya, Orsina, Orsa, Ursa, Ursulina, Ursuline, Ursola, Ursella, Urselina, Usulie, Ursie, Urska, Urszola and Urszuli. Ursula is related to the even more rare Ursinia, which includes Ursina, and is the botanical name of the "solar fire" plant, Ursinia anthemoides, which looks like an orange daisy. Ursinia is a variant of Ursula, created by botanist Joseph Gaertner in honor of Johann Heinrich Ursinus who lived in the 1600's. The boy's name Orson also means "bear."
I would immediately blame Ursula's decline in popularity on Disney's "The Little Mermaid," except that movie came out in 1989 and Ursula was already on a downward slope. In 1983 Ursula ranked at #984 and has not been back on the SSA list since. Before her disappearance Ursula had been given since at least the 1880's in the U.S., with high points in the early 1900's and the late 60's/early 70's. Currently Ursula is given to less than 30 baby girls a year, at its lowest point since the 1880's.