Why does sp_rename not affect the output of sp_helptext?
Don't know why but it is kind of documented.

sp_rename (Transact-SQL)


  Renaming a stored procedure, function, view, or trigger will not
  change the name of the corresponding object name in the definition
  column of the sys.sql_modules catalog view.


sys.sql_modules is a view that uses the base table sys.sysschobjs. sp_helptext uses the view syscomments that in turn uses the base table sys.sysschobjs.