Hi Lewis,
You need to give it a little bit of time, you need to teach Google that your brand is "pea soup digital" the more you go out and tell the world this the more Google will learn that is your name.
How do you do this I hear you shout at your monitor? Well you can do this via backlinks, social (Who doesn't love talking about pea soup!) and anything else you can think of that just gets your name out there.
Take a look at some of these to give you a head start -
http://moz.com/blog/using-modern-seo-to-build-brand-authority
http://moz.com/blog/4-ways-to-build-trust-and-humanize-your-brand
http://moz.com/blog/social-norms-build-a-strong-brand
And much more!
The reason Your privacy policy is ranking higher is firstly you're new and subject to change so don't worry it will change, it could be it has some more content and Google thinks that is what the user is looking for when searching for the term. Work on your brand and it will turn around (or look into a bit more content explain why your the best pea soup in town on your homepage)
tl:dr - Give it some time so Google can understand your brand terms, while you are waiting create some back links (My pro tip is do this why listening to /journey "don't stop believing" ) get people talking about you.
Hope that helps and all the best.
P.S you've got the rel=publisher which is a great start!