You can't do anything to clear it from your name. In the past it was possible for minor records to be deleted from the Police National Computer, however these days, the police only delete the record when you are deemed to have reached 100 years of age.
There has been some debate about this. Last year, discussions took place which could have resulted in the deletion of thousands of criminal records. However, 5 chief police officers appealed this decision on the Court of Appeal and they won. They won the right to keep records of people who have committed even minor crimes up until thier 100 birthday.
So you can't have your record deleted at the moment.
However, there is a review currently underway, which is due to be handed to Alan Johnson, the home secretary by the 26th of February this year, which looks into how criminality information is shared between frontline organisations and agencies such as the CRB.
This covers a wide range of topics including whether records should be deleted and under what criteria they should be deleted. It also includes giving patial access to records held on the Police National Computer. This should be of interest to you.
Hope that helps.