As I see on your screenshot you use license number for unit's names , so the customer can see on the map name = license number + unit icon
Why is it not attractive or clear ?"
Some clients do not want to see the Icon, just the license and the arrow. And more if they are used to other platforms which had this option...
as for other issues it's not still clear to understand : what do you mean to add different names in the map on the left side ? Which left side? would like to see the another unit's name on the map than in the monitoring list? what is a reason for it?
Reason, as you know they can name the truck/van/car/pet by nick name, number of truck, license, driver...and who knows how more, that is why, as more options we could give as better.
btw, the icon (real photo) in the Satellite view from Google maps, i the APP is not good seen. test yourself.