How did Sai Baba get his name? Was that his given name?

The name 'Sai Baba' was bestowed upon him when he arrived in Shirdi. The Introduction (Chapter 0) explains that when Maharaj, wearing a kafni and cap, entered the Khandoba temple, a resident named Mhalasapati greeted him with the words 'Aavo Sai Baba,' which means 'Come, Sai Baba.' Maharaj embraced this name for the rest of his life. This is confirmed by an account where, during a commission testimony, he was asked his name and he simply replied, 'They call me Sai Baba,' indicating it was the name by which he was known.