I just tried to create a driver's account on Lyft's website. There's an initial page where you give them your name. And then, deeper into the process, a form for supplying your name as it officially appears on your driver's license.

Which makes sense. There's likely a lot of drivers who want to go by "Tom" instead of "Thomas" or whatever their full official name is – which is even more important for drivers with very uncommon names who want to go by something more familiar/pronounceable. There's probably a decent safety argument for not requiring drivers to have their full real names be accessible to the user, especially in cases where a driver has an uncommon (i.e. easy to doxx) name.