To edit the paddock order (or any farm map setting), you must be either a Full Access or Authorised user.
To edit your paddock order:
Select the "Paddocks" button on the left-hand menu.
Select "re-order paddocks" in the top right of the paddocks modal.
Click and drag to re-order paddocks to the desired order, or click the arrows on the right-hand side of each paddock to send to the start or end of the list.
Once you are happy with the order of the paddocks, click the "Save" button.