You can check Managing your billing information · Shopify Help Center
My name is Lilith, I'm on the Social Care team at Shopify.
We have a great step-by-step guide on how to edit your banking information for your Shopify Payments processor.
You'll need to enter your old banking information in order to change to the new one. This is a security feature to prevent the possibility of anyone changing it without you knowing and hijacking your account. Security is important!
A quick note though, if you're not using Shopify Payments, then you'll need to change your banking information on the 3rd party payment processor.
Since you're changing some banking information, it might be a great time to bring up some finance tips. As your business changes and grows you'll want to have access to more funds to continue expanding your brand. We've got a blog post here that helps break down some ideas on small business funding that are beneficial for many small businesses.
Along with good funding, be sure that you are comfortable with your accountant so that you can take advantage of any of your local tax breaks for small businesses. Don't forget to track your numbers with good accounting software to make both you and your accountant's tax season go smoother.
Let me know how you do with the information above! I'm happy to answer any questions you think of as you work on your business.