What exactly was the promise made at the end of the first chapter regarding the name 'Hemadpant'? The text in chapter 2 is vague.

You are correct that the provided excerpts from Chapter 2 are intentionally retrospective. The text states, "At the end of the first chapter, I promised to tell The story of how I was named 'Hemadpant.'" This confirms a promise was made, but these specific source chunks from Chapter 2 do not contain the text from Chapter 1 or the exact wording of that original promise. The purpose of this mention in Chapter 2 is to fulfill that previously established commitment and to satisfy the listener's curiosity, which the author states is also an inspiration from Sai Baba. The narrative pauses to tell this backstory before continuing with the main life story of Sai.