OP... From Uber's stand point you can absolutely do this. In the UBER website dashboard there is a "Banking" option where you originally entered your ACH for your bank account under your social security number. You can change your settings in there.
There are benefits and liabilities to doing this under a LLC, or corporation. For me, I have another business that is closely tied to this -- and I have mine going to the same LLC. I run the other one as a paperwork loss, so from a tax stand point, I can offset most if not all of the uber profits (as much or as little as it may be), with the loss from the other business model.
The best advise someone could give you is to go talk to a tax accountant/tax advisor -- not a bad idea regardless to learn the many deductions that you can claim against your rideshare income to reduce your tax liability.