As a man's name, Ara is Armenian, possibly of Sumerian origin. There is an Old Norse element arn which means "eagle" and is found in names such as Arnold and Arvid, and it's possible that Ara could be a short form of names containing this element. However, I can't find any women's names in use that use this element.As a woman's name, it is likely a modern invention, possibly a short form of Arabella, or inspired by Sarah/Tara/Dara/Mara rhyming names. Though Ara has been quietly used for women in the USA since at least 1880, Variations like Aira, Ayra etc. started becoming popular in the late 20th century, following the rise to popularity of similar-sounding names like Ariel and Ariana.
See Also: Aarah, Aara, Aira