Page Titles are by far one of the most important elements of on-site SEO. They should include your most relevant keywords for that particular page or article. Still today I see many websites that use only their company name in their page title. Please do not so this unless your business name is the only keyword viewers will search for. Your keywords should be the first phrase. Also, do not make the mistake of keyword stuffing. I have seen many sites that will put all of their keywords in their page title, this is called keyword stuffing, and Google is well aware of keyword stuffers. If you include too many keywords, it dilutes their importance. Try to keep your page titles around 70 characters, much more than this may end up hurting your page ranking.
Joomla 1.5 provides an easy way to modify and override your page titles from the menu manager. When you click on your menu items from the menu manger, you'll see a tab called "Parameters (System)." Here is where you can override the titles for articles and some components. Put your new title in the Page Title field. There is also an option to "show the page title." You can use this to add this title to the article heading. If you choose to show this on your article heading, you should disable the title field in the article item. Otherwise your article will have two headings. Most of my articles are named the same or similar to my page titles, so I choose not to show this within my article.