Elon has said more than once it will work perfectly fine, even when the van (or yacht, or train) is in motion. In the Starlink Engineers AMA on reddit the team

Elon has said more than once it will work perfectly fine, even when the van (or yacht, or train) is in motion. In the Starlink Engineers AMA on reddit the team said they're working on reducing the power requirements. My current vehicle has 200W of solar, but a 100W draw would be a lot.