No, the driver cannot see your phone number.
After you've requested your Kapten, you can see the details of the driver (name and licence number) as well as the vehicle details. From within the app, you can also call or text your driver but rest assured that your number will be masked. Your Kapten driver will equally also be able to contact you through their app and their number too will be masked. You can contact the driver up to 1 hour after the ride has ended.