If the part already exists and has the correct filename (serial number) then when the drawing is created it should take that name as the default name for the drawing.
This may not happen if you have some settings to the contrary like assigning the filename of the drawing - see EPDM Options in SolidWorks Addin Menu. You must let SolidWorks 'decide' what to name the drawing and not EPDM.
If you just want to rename the drawing to match the part then that can de done as a combination of passing variables between the part and the drawing and then using a Dispatch script to rename the drawing at an appropriate time in your Workflow.
Note the 1st and 3rd lines for 'sharing' the variables - understand that the variablies in the drawing are ONLY updated if it is checked out, regenerated and saved - then checked in. Meaning that your rename (if done using Dispatch) has to occur at the earliest after your first checkin of the drawing.
Thanks Tim I'll look into this