Florida does not have any guidance on this point; I doubt that any state does. Beyond that, you're asking for help interpreting forms that only you have read.
Two observations: 1) "Ownership" generally has nothing to do with safe deposit box operations. A customer may lease or rent a box, but he certainly does not own it. 2) If your system is allowing you to insert the labels you put on customers then use the same terms that are found in your lease or rental agreement.
People who rent safe deposit boxes are often referred to as lessees, tenants, or renters. People who have the renters' permission to enter a box, but are not a party to the contract are often referred to as deputies.
In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.