First of all ---Sole proprietor NAME you register as WHAT ?

It can be your own name or any other ABCD name

If register using your own name in SSM ( because it is cheapest ) -----of course the bank account will also need to use the same name ie your name . ( This is what I actually do for my business ---everything goes into my personal account )
If you register under a different name ( other than your name in SSM ) of course your bank account will have to be different lah ---like ABCD or something else