If his step daddy actually adopted him in Indonesia is it’s unlikely that his his legal name in the US was ever Soetoro.
I think it’s more than likely they just put Soetoro on his school forms in the paternalistic Islamic society of Indonesia. That would technically be fraud.
Hard to know anything for sure without his records.
I do not suppose that we will ever know much about him. I believe that all his records have been destroyed. (sanitized by pros)