Yes, and it's more common than you think. For example, if you are moving a vehicle on behalf of someone who has entrusted you to set up the shipping for them, it’s just fine. When you sign our terms and conditions, you certify that you are allowed to do so.
This is not uncommon at all. There are several valid reasons that you would ship a vehicle that is not under your name. The most common is usually that you’re setting up transport for a friend or family member.
A great example that we see all the time are parents sending their kids to college. The vehicle is registered under the son or daughter’s name name but the parent is paying for and arranging the auto shipping.
Please note there may be occasions where additional verification may be needed.