Just to be clear, which of those assertions is backed by a document you can either refer to or share with, and which is just a reasonable deduction or good guess?
The part about Anna Toot comes from Obama’s relatives in Africa that is the name his mother told them and by which they refer to her as per an article written there.
Obama’s family tree lists an Anna Toot as a direct ancestor on his mother’s side, so it is not a name taken from thin air.
Without a copy of the Original marriage certificate, the Original divorce decree and of course the first Birth certificate it is all reasoned speculation based upon the written words of Obama and his family in books and articles.