I have an EZ-Pass and a FastTrak and use them on rental cars all the time. It only takes a few seconds to bring up the phone app for the California tag and to enter the new plate and just a bit longer to use the web browser to bring up EZPass for Virginia.

I run between California rentals with no car denoted for it. However, the company has a truck with VA tags registered and this thread has me thinking that I might not need to bother to add the rental in that case. I will test it in VA since there is no problem using my Florida SunPasses on rentals without registering them since I have a car on each.