The Driver shown on the schedule section of the Operations screen is originally pulled from the default driver set on the vehicle.
However, the driver on the schedule will be updated to show the last driver that logged into that vehicle on a tablet device.
Example:
Vehicle Skip3 has a default driver of "John Smith" - "John Smith will show on the Operations screen by default
Driver "Daniel Jones" logs into that vehicle on his tablet to see what jobs John has - the Operations screen will now show "Daniel Jones" as the driver
Driver "John Smith" logs out and back into that vehicle on his tablet - the Operation screen will now show the driver as "John Smith" again.
There is no way to update this driver from within the application. The only way to show the correct driver is to make sure that they are the last person to log in to the vehicle on a tablet device.