Does anyone know what determines the order that matrix options are used in the Matrix Item Name Template? For example, it keeps wanting to do "{itemid}-{color}-{size}" but client would prefer "{itemid}-{size}-{color}".

Use the MATRIX ITEM NAME TEMPLATE field in the accounting tab on the parent item

Yes, I know you can manually change that template on a per item basis. And I can even manipulate the field via a workflow to achieve the desired effect. But, I am curious if there is a way to control what order the matrix options are used by default.

I think it goes by the internal id of the options