I can't think of a reason to include your website address in an H1 tag at all. H1 is intended to indicate the topic of the content on a page; it functions as a headline similarly to how a headline on a newspaper page works. That's why it's a somewhat decent place to place keywords—it indicates to search engines what the page is about.

For a homepage, I'd recommend using your brand name, in text. If there are other relevant keywords, use them as long as it appears natural and informative to visitors. But actually placing your URL in an H1 is unlikely to have any value for you.

You might want to check out the Beginner's Guide to SEO. This Visual Guide to Keyword Targeting and On-Page SEO could help, too.

Hi Jay! Did you get this worked out?

I love the answers you've already gotten, and as I so frequently do, I recommend checking out Cyrus Shepard's "Keywords to Concepts" to get an understanding of how topical search works. Yes, the keywords you've brainstormed may individually have low search volume, but you may find there's a lot of potential organic traffic outside of those terms.

Hi Kevin! Did this work out?