Since Deployment Solution 7.5, computers rebooted to Automation are renamed to their serial numbers rather than "MiniNTxxxx".
To retrieve the computer serial number, while in automation, type on the command prompt:
"wmic bios get serialnumber"
Then, lookup the computer on the console under Manage > Computers.
Instead of adding a Search custom criteria, that should help to quickly identify the target machine for troubleshooting purpose.