Yes! You can prioritize the order in which tags appear on your roster. You will need to have the proper permission to reorder the tags.
To order the ranking of tags, head to Configuration > Tags. Click Reorder Tags, and then you can drag and drop the tags to reorder how they will show on a customer's account and in the roster. Once your order is set then click Save.
On the customer's profile and reservations, the tags will now show in the order you set as a priority.