If I give someone my bank account, and they ask the bank who is the owner of this account .. Will the bank give them my name?? If so how can I keep my name private?
You mean the bank account number (to transfer money)? I don't think so, but give them a call and ask them. Different countries / different regulations.
corey bryant is right. It depends which country you are in. Im in the USA and here I do not believe they can give out that kind of information. If someone is going to do a transfer to your bank account they will probably need your bank account number and name, the bank won't just give some stranger personal information of one of their customer's.
Banks would not be so quick to reveal any details so easily. However if he do a counter deposit into your bank account, he would get a deposit slip which should print out your name. In fact, come to think of it, when I do a counter deposit, I need to fill in my name in the deposit slip and if I don't, the bank teller will fill in the name for me. Besides why do you want to keep your name private if you are doing something legal ? The more you hide from your customer, the more they will feel suspicious about you.