Yes, you can do this by selecting a Re-open status.
Re-open status is the value that a pre-selected state picklist field with closed states configured, takes when a record is re-opened. The re-open status must be configured for all the modules.
For example, the pre-selected state picklist field in Contacts is Status. When you select ‘Cold’ as the re-open status in Contacts, every time you re-open a contact, the Status field's value is set to ‘Cold’.
Follow these steps to select the default re-open status: