Booking is not a quick process and the jail runs it at whatever pace the staff and the system allow. After an arrest, the person is transported to the facility, and then the processing begins: identity verification, fingerprinting, photographing, entering charges into the system, searching for outstanding warrants in other jurisdictions, health screening, property inventory, and classification. Each step takes time and they happen in sequence.
Busy days, shift changes, high intake volume, or situations where multiple warrants need to be resolved can all slow the process down significantly. A person arrested at 2pm may not complete booking until late evening or overnight. That is not unusual and does not signal that something is wrong.
Once he is fully booked, the information will update in the jail's system and become searchable in the online roster, though even that can take a few additional hours to reflect after the physical booking is complete.
He is in law enforcement custody and being processed. He has no control over the pace of it, and neither do you. The wait is frustrating but it is the normal experience.