Um ... simply renaming "Processing" to "Complete" is really not solving the problem.

If a customer places an order and it's immediately set to "Complete" status, that's really *not* the truth.

A better solution would be to write custom code to have your ERP system update your store data with a added status-history entry to state that the order has been completed, perhaps along with shipping confirmation/tracking details. As I said, that will require custom coding.