Maryam Uz Zamani Begum was a daughter of Raja Bharmal of Amber and she was (unwillingly) given as wife to Akbar in a strategic alliance for the safety of Amber and his people.
The real name of Maryam Uz Zamani Begum is neither recorded in Mughal History not in any authentic sources of Amber. Her real name just disappears from history. It's alleged that her name was either Harka Bai or Hira Kunwari.
The reason she is often associated with misnomer Jodha Bai because James Tod in his book confused Jagat Gosain, princess of Jodhpur and wife of Salim with Maryam Uz Zamani Begum, wife of Akbar and since then the mistake is often shown in movies and serials.
Maryam Uz Zamani Begum had many titles like Wali Nimat Begum or Malika-i-Hindustan. Her chastity and loyalty is praised in Mughal Sources. However, the marriage stil was a strategic alliance only. His favourite son was Sahzada Daniyal and not Salim, son of Maryam Uz Zamani Begum.
Akbar had a wife whose name was Arif Un Nisa Begum and her origins are not known. She is mentioned as Akbar's Jauza (Wife). She is shown with a sword and a shield. Probably, the warrior qualities of Arif Un Nisa Begum are given to Maryam Uz Zamani Begum in movies and TV serials.