The name could be of a few different etymologies depending on the bearer of the name.
In Hinduism, it is an epithet for the goddess, Parvati, said to be derived from the Sanskrit exclamation, उ मा (u ma) meaning, “oh don’t” a reprimand from the goddess’ mother from severe austerity.
It could also be a Hebrew name meaning, “nation.”
The name is currently very popular in Bosnia & Herzegovina, coming in as the 81st most popular female name, (2010). In this case, the name may be a borrowing from the Sanskrit or it could be a short form of the Bosnian female name, Umihana, which is a Bosnian form of the Islamic epithet, Umm-ul-Banin, meaning (mother of several sons). Umm-ul-Banin was the epithet of Fatimah, the second wife of Ali. Another Bosnian form is Umija.
The name was brought to the spotlight, in the Western World, via American actress, Uma Thurman (b.1970). In the actress’ case, she was named for the Tibetan Dbuma Chenpo, the db being silent.