Unfortunately we can't create drawing relations. But if the parameter &dwg_name exists in the part, you can create a part relation that truncates it and creates a new parameter that you can reference as the drawing name:
new_name=extract(dwg_name,1,3)
In parenthesis is the string name, the position to start extracting from, and the number of charaters to extract (including the current postion). So, in the example above, if dwg_name is ABCDEFG, new_name will become ABC.