I don’t know about the name changing BL as I can’t access that part of my Humminbird account right now… I guess that he could and as long as you had the User ID and Password you could use the account. You should register the unit for yourself though so that you will get any automated email messages.
Whether you register the unit on the Humminbird web site or not does not affect its warranty (unless it is the additional warranty through the Humminbird Select program). You would still be required to show proof of purchase from a retailer.