The information under your website link is called a snippet and the information contained in the snippet varies depending on the search engine but the majority of the snippet comes from the meta description tag found near the top of the html of each page. Google and Bing tend to construct the snippet entirely from the meta description tag if it was written in such a way that it compliments the written content of that page. Yahoo may more often use some of the meta description and some phrase from the page that includes the keyword that was searched for. It is also possible to get different snippets for different keyword searches even though the same page comes up in the search results.
All of that is the long way of saying that the fastest and easiest way to change your snippet is for your or your web designer to change your meta description tag. The meta description tag should stay within 250 characters, should broadly describe the theme of the page, and should incorporate your target keywords (as opposed to the page’s title tag, which should stay withing 80 characters and should concisely state the thrust of the page as well as incorporate your keywords).
In the description tag, you can put your company name near the beginning if you choose to and it should show up in your snippet–that way, you don’t have to use up any of your 80 characters in the title with your company name.
