You can start ranking for your business name by including your business name in the page title and meta description of your home page and every page of your website where it makes sense (easy if you’re using Shopify, Squarespace or WordPress with the Yoast plugin).
And If and when you get more inbound links to your website, try to make sure the anchor text (the actual words that are linked) is your business name (and not, for example, the words “click here”), like this:
Melissa McGraw is an SEO consultant who owns The Creative Potential.
Ranking for your business name isn’t always as easy as it seems. If you have a generic business name (like I do!), you’re competing against generic searches for that same term. So you might try to these variations to ranking for your biz name:
your business name + the industry (“the creative potential search engine optimization”)
your business name + products & services you sell (“melissa mcgraw seo consultant”)
your business name + location (“the creative potential new york city”)
your business name + owner name of biz (“the creative potential melissa mcgraw”)