The problem is not the named database then -- it is the ODBC Engine DSN. From the Tools menu of the Pervasive Control Center, start the ODBC Administrator (32-bit). Find the Engine DSN's that have the SAME NAME as the named databases you have already deleted, and delete them.
You can prevent this in the future when you delete a database within the PCC -- be sure to check the box to delete the ODBC DSN at the same time.