Ideally you would take Collagen on an empty stomach as this will mean you will have less stomach acid to break down the active nutrients and proteins. However this is just an ideal scenario - you do not need to take collagen on an empty stomach to obtain the benefits.
Last thing at night is a good time as your body can absorb and use the collagen at a time when it is actively repairing anyway - i.e. when you're asleep. However if this is not convenient then use the supplement at the best time for you to be able to take it regularly.