The Database TraceListener calls the WriteLog and AddCategory stored procedures when data is logged.
So you just want to log the distinct category names? You don't want to log the messages? Or you don't care what category the message belongs to?
If you wanted to do that you could modify the stored procedures. Basically change WriteLog to not insert a record always return a value (e.g. 1) and then modify AddCategory to not call InsertCategoryLog.
I feel like I'm not 100% understanding the scenario -- if you explain the scenario in more detail perhaps we can provide more details?
Enterprise Library support engineer