You can change the order that the staff appear on the Client Scheduler as well as in the Staff dropdown when adding appointments. This can only be done by staff with a security status of Account Owner or Administrator. In order to do this, you'll need to go to Settings > Staff and toggle the Reorder switch to On -
You can then reorder your staff alphabetically by either the name or the internal name by clicking on the Reorder Alphabetically button -
If you want to reorder your staff in a non-alphabetical order, you'll need to hover your mouse over the 
button to the left of the staff name. When the cross arrows appear, left click on them and drag the staff to a different spot -
Once you've reordered the staff to how you want them to display, toggle the Reorder switch back to Off -
You will now see that the staff display in the order you set them on the previous page.