Glad to know, you have created a website and its on web.
Coming to your query, to show Company Name and Links on Google search, there are many steps and sufficient traffic needed.
To list company according to search, you have your Company verified in Google+ using Local Business Page. As well your website must be linked with Page. Generally this wont work, Google search at WikiPedia or other large scale database for Listing details if not a local brand.
In case of Contact Us, About Us Page etc listing just below company name, use Sitelink schema of Google and submit a structured Sitemap of your website to search engines.
This entirely depends on what platform you are using for creating website. If you are going with normal ASP.NET website or HTML website, then it is very hard to describe all SEO steps here.
Kindly take help of any SEO consultant. You can contact our Web Master Tony John who is SEO Expert having nearly 20 years of experience in Web Designing and SEO field. http://www.techulator.com/
Glad to be,
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