The text says Sai Baba is 'distant and detached from his name'. Doesn't this mean he was indifferent to his devotees and their problems?

This is a misunderstanding of his divine nature as described in the Shri Sai Satcharitra. While Chapter 36 states Sai Baba is 'distant and detached from his name' and 'indifferent to the "I am He" (So-ham) attitude,' this refers to his egoless, transcendent state beyond worldly attachments. The very same chapter clarifies that this detachment does not equate to indifference towards devotees. On the contrary, it explicitly says that for those who sing his praises, 'he never lets them lack anything; he protects them completely' and 'he calls out to the poor and weak, fulfilling the desires of all.' His detachment is from ego, not from his followers' welfare.