Hi guys, I had the same question and this thread had the answer: https://community.shopify.com/c/Accounting-Taxes/Stuck-on-Credit-Card-Processor-section-of-CA-Sellers-Permit/td-p/444766
Merchant Card Processor Name is simply “Shopify Payments”
Merchant Card Processor Account is simply your Shopify ID which you can find on your admin page on the top right by clicking “Manage Account” and looking at the URL. It should look like https://accounts.shopify.com/accounts/<id>