Each site can have a name. For example, site x. Each page also can have a name (or a title) that should appear in <title> tag in the header. However, many websites out there use the combination site name - page name to provide the value for <title> tag. I find it a little far from being semantic. On the other hand, if you only include page title in <title> tag, search engines won't find your site by its name. For example, if your site's name is Thought Results and you don't include it in page titles, then if you search for Thought Results, you won't find your site in SERPs.

Thus I'm searching for a mechanism to both include site title (not page title) in every page, and also only include page title in <title> tag to get more semantic results.

Is there any way to achieve this?