No, not your paypal name but when you add bank account, it asks you to specify name of bank holder, this name should match with your bank account holder's name. But if it don't, money will get transfer to miscellaneous account of bank. You need to verify in that case with your bank account to transfer money from there. But why you created another paypal for that, you can just add another bank account into same paypal account. Also you can remove and re-enter same account with name of bank holder's.