Rani (RAH-nee) is a Hindu girl's name, Arabic, Sanskrit and Nepali for "queen." As a word, it is the feminine form of Raja or Rana, which applies to male rulers. It is still used as a given name today in India. Some sites will tell you Rani means "she sings," but in Hebrew it is a nickname for the masculine name Ran, meaning "he sings," which is where the common misunderstanding comes from.
Rani has dozens great namesakes. Because Rani is also a title it's a bit hard to siphon out the namesakes where Rani is a given name. Rani Vijaya Devi is one example. She was a princess in India, but articles do not specifically point out her birth name.
Rani Rashmoni founded the Dakshrineswar Kali Temple and played a part in blocking British trade on the Ganges river. Rani Karnaa, born in 1939, was a dancer who was so respected that she recieved the Padma Shri award. There was also a famous Pakistani actress called Rani, and Indian actresses Rani Agrawal, Rani Chandra, Rani Chatterjee and Rani Mukerji.
The god Krishna's consort, queen Radha is sometimes referred to as Radha Rani or Radharani, and therefore the name can be given in her honor.
In the U.S. Rani is rare, given to only 25 girls in 2016, but it has been used since 1946, and 44 times in a year was the most it was ever used.