The move by Warwickshire Police is aimed at encouraging the public to report anyone who is breaking an Asbo.
The force said it also wanted to alert people to "the unacceptable conduct of these people in the past".
The naming-and-shaming trial covers the Warwick and Stratford-upon-Avon areas and currently features 13 people subject to Asbos or criminal Asbos.
If the trial is successful it could be extended to the entire force area.
Asbos are issued by civil courts and generally ban offenders from carrying out certain nuisance behaviour for a period of time.
Criminal Asbos are issued when criminal behaviour is also anti-social and orders often ban people from meeting certain friends or entering certain buildings or areas.
Warwickshire Police said the orders are only sought as a last resort.
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