If the arrest was recent
Start with the county jail
In Utah, someone who was just arrested and not released is held in the COUNTY JAIL run by the county sheriff, not a state prison, so the UDC Offender Search will not show a brand-new arrest (UDC's tool explicitly excludes people held pretrial in county jails).
Utah participates in the national VINE system (Utah VINE), a free way to check custody status and register for alerts by phone, email, or text (search at vinelink.com or use the VINELink app).
Many Utah county sheriffs also post an online jail roster / inmate lookup.
For a very recent booking or bail details, call the county jail's booking or records line.
County jails are run by the sheriff in each of Utah's 29 counties; many post an online jail roster. Use the county sheriff's roster or Utah VINE, and call the jail's booking/records line for recent bookings and bail amounts.