I ran into the same issue using Microsoft's SMO objects in C#.  I opened a case with Microsoft and they confirmed that there was a bug.  As you discovered, the problem is that when you rename an object whose definition is contained in sys.sql_modules the object gets renamed in sys.objects, but the source code is not modified in sys.sql_modules.

Interestingly, the people responsible for SQL Server Management Studio have "fixed" the problem in their code.  Whenever you script a stored procedure through the right-click menus the new (correct) name appears in the script even though the old name appears in the sys.sql_modules record for that stored procedure.  Apparently, they rebuild the definition line up to the AS keyword and then concatenate the rest of the script from sys.sql_modules.  What a kludge!!!

Why not fix the underlying problem?  When you rename an object whose definition appears in sys.sql_modules, replace the old name with the new name in the object definition script in sys.sql_modules!