Can we create separate document styles for SPO and BPA backed SPO with open orders in system?

Summary: Currently we are using the standard style(Standard Document Style) for standard purchase orders and blanket release purchase orders. For both the purchasing documents the system displays the label as "Standard Purchase Order" only. Now the customer needs to differentiate the SPO & Blanket release with separate document style labels for each. But there are open documents for both the Standard purchase order and Blanket releases. Also, note that we have used the approval conditions based on the document style "standard purchase order", which will be impacted in case we change the document style label.

Is there any simple way to segregate the display label name without disturbing the approval rules and open documents?