How to rank #1 for brand name when its 2 competitive keywords?

[Silkstream]

Hi Mozzers,

I have recently began the SEO on a website which is a few years old, with little SEO done beforehand.
I really want to get this domain ranking #1 for its brand name, however the brand name also happens to be a combination of two highly competitive keywords - one of them being "hire".

I have done everything I can think of as a recommended step to signal Google, but it still sits between position #20 and position #15 (on a good day).

So far I have:
Set up G+
Linked the website
Added Rel=publisher
Submitted site to Yell.com and a couple of other business directories
Added branded links from every the bio of each article on the blog pointing to the homepage.
Built a handful of branded links from related niche websites.
Set up social pages.

Question:
What else can I do to improve on its position in the SERPS?

More info:
The site ranks number 2 in Bing for the brand name. The domain is an exact match of two keywords without a hyphen between them - the site ranks position #1 for that search on Google.

Question:
Would a hyphenated domain make any difference at all?

Thanks everyone!

[David-Kley]

"What else can I do to improve on its position in the SERPS?"

Backlinks, backlinks, backlinks. Validation, validation, validation. There are a ton of citation sources available, and I would submit to as many of them (that are reputable) as you can. One thing to remember is: don't only link to the homepage if you want the subpages to get some good ol' Google love.

"Would a hyphenated domain make any difference at all?"

If you already have a good domain in place, I would not go changing that. The existing domain name probably has domain age and history, along with backlinks in place. Only if the existing domain had a spam or penalty issue would I change the domain.

Be patient. The changes will not come fast. Google has to validate your new information from each source, and that can take a while. To speed it up a bit, link out to your social and ciation sites (using a nofollow or not, up to you) as they will link back. Once you have the new links in place, submit the URL with the outgoing links in GWT using fetch as Google. If it is a legit business, submit to major data providers such as Axiom, since Google uses them for data validation. You will need a tax ID and some other information tho.