We have a smaller umbrella that we stick into the trunk side strap with a shopping bag, but it's not as neat as that.
I did also buy one of these to fit in the top door pocket for the drivers door. This is a very small umbrella for actually keeping the rain off when opened, but it fits that upper pocket very well.
We have a container placed at the driver's side for our front umbrella too. Our umbrella is not as small, versatile and portable as yours, but we got it free (so better not complain)
The container helps it from sliding all around when driving spiritedly. Its secured with velcro provided by the vendor