How to change my business name and URL without errors?

[MSchaffer30]

Hello all, I am changing the name of my business and want to make sure I don't screw anything up on the Shopify side. Is it as simple as changing the store name in the settings?   I already have the new URL and will redirect the old one.  Will it create a bunch of 404 error pages in my indexing or will all that be automatically updated?

Thanks!