Ash here from the Shopify team.
This is a great question, and I'm happy to help out! When applying an author to your blog posts, you'll be able to select from the list of staff members active on your shop. So one option for having your business name appear on your blog posts as the author, is to create a new staff account with that name. Once that new staff account is active, you'll be able to select it as your blog posts author. Here's a screenshot showing how to select an author when editing a blog post:
Another solution would be to edit the coding in your theme so that there is a blog post author hard-coded into each blog post, rather than having the author name pulled from a staff member. If you prefer this option, our team may be able to assist, but I'd need to know what theme you're currently using. A Shopify Expert would also likely be able to assist with this sort of code work, should it end up falling outside our teams scope of support. Shopify Experts are trusted, third-party agencies and freelancers, who are available for hire by Shopify Merchants. You can visit their site here to contact an Expert, or post a job request and receive quotes from eligible Experts.
I hope this is helpful, and feel free to reply back here and let me know what theme you're using if you'd like me to take a closer look into the possibility of our team performing the code solution.