It is sometimes claimed to be a feminine form of the Basque masculine name Inar, with the meaning "ray of light", or a feminine name of Arabic origin with the meaning "heaven sent". Both of these origins, however, seem suspicious at best.
A city in Italy bears this name, though in this case it originates from Latin Mediolanum, perhaps ultimately of Celtic origin meaning "middle of the plain". In some cases the city name may be an influence on the use of the given name.