One branch did insist on knowing my name, the client was paying in the full fee and I suspect if he'd just paid in the deposit amount he'd not have been asked to phone and ask for my name.
I did give my name, nothing scary has happened.
I also once had to refund a deposit by bank transfer, that would have revealed the name on the account. At the time the client deserved the refund and the chance he might do something with the account details was secondary to me needing to be professional.
Amazon gift card is another option.
AW do not allow their credits to be used to pay for a booking, Paypal has rules about use for adult services - it's also reversible.
I've taken numerous deposits into my bank account, so far apart from the incidents I've described there's not been any problem. The main issue are those who say they are going to pay the deposit, then either don't or take a long time to do so. I now make it clear only contact me when you are ready to pay the deposit, otherwise you are wasting your time.