You do nothing until an offical order has been entered by the circuit court granting your petition for a name change.
Once the above has occurred and the name change is then official, there is no particular order of contact as far as I am aware to apprise agencies, entities, or others as to the change, but you might want to start with the DMV(if you have a driver's license) and the SSA regarding the name change, and your local taxing authorities.
