Who will be the “bookkeeper” for my HSA?

You are the "bookkeeper." It is your responsibility to keep track of your deposits and expenditures and keep all of your receipts (necessary if the IRS audits you). It is also your responsibility to adhere to the regulations governing HSAs and payment of qualified medical expenses. American Fidelity does allow the option to scan receipts into their system and will save them for you should you ever be audited.