What is the origin of the name 'Sai Baba'?

The name 'Sai Baba' was bestowed upon Maharaj when he first arrived in Shirdi. As detailed in Chapter 0, upon arriving with a wedding procession, Maharaj went into the Khandoba temple. There, a gentleman named Mhalasapati saw him dressed in a kafni, a cap, and a dhoti. Upon seeing him, Mhalasapati instinctively welcomed him with the words "Aavo Sai Baba," which means "Come, Sai Baba." Maharaj held onto this name for the rest of his life. The text notes that when his testimony was once taken in a commission and he was asked his name, he simply replied, "They call me Sai Baba."