Using some SEO controls for WP, it is possible to add a fixed value (such as the site name) + a separator (such as a dash) either before or after the custom doctitle.
However, with WordPress SEO, entering any value as a custom doctitle clears templates previously set, so you can't do it with templates.
Is there a way to add a fixed value like the site name, a separator, and specify whether to put it at the end or beginning of the custom doctitle? I haven't found a way to do this. If not, I think this would be a good feature to add.
You could get doctitles like the one below. Otherwise, one would have to consistently type the fixed value and separator on every post or page.
Test.com, the testing specialists - Our Custom Doctitle on Something