Is Jodha Bai wife of Akbar?

Akbar married the daughter of Raja Bharmal of Amber but there is some confusion regarding the name of this princess. According to the movie Jodha Akbar, Akbar's Hindu wife's name was Jodha Bai. Akbar's son Jahangir married the daughter of Raja Udai Singh of Jodhpur. Jahangir gives her name as Jagat Gosaine. She was called as Jodh Bai since she was the princess of Jodhpur.