They usually call it booking or the booking area , and the place is often a jail or a police station where the intake happens.

In some cities, people may also say central booking , which is a local processing facility used after an arrest.

Simple wording

  • Booking = the process of recording an arrested person’s information.
  • Jail / police station = the place where booking usually happens.
  • Central booking = the name some places use for the intake site.

Example

“After the arrest, they took him to central booking.” TL;DR: The common answer is booking , usually at a jail or police station.