Yes most times money orders are anonymous but they can be traced back to the person who the money order is written out to and who cashed it.
But money orders usually can't be traced back to the person who bought the money order or filled the money order out.
But sometimes some money orders may be able to be traced to the person writing it but usually not.
It depends on where you bought the money order from.
As long as you don't give out any identifying information on the money order though then it usually cannot be traced back to you.
However like I said the money order can be traced to the person cashing or depositing it since the money order can only be cashed or deposited by the person who the money order is made out too.