I've been wondering about this for a while but never come across a solid answer.

Many websites include their name in all the title tags of their articles. This is often apparent in word-press blogs etc.

eg: Tsunami hits Japan and leaves thousands homeless | My Website Name

The issue I have is that Search engines strip the stop words out of this sentence to leave the words in which it compares to the body text.

So if I want my article to rank well and be relevant, in this case about the terrible Tsunami that has recently struck Japan what is to STOP the MY WEBSITE NAME section of the title de-valuing the relevance of the article.

Am I over-worrying? Or should I take this in to consideration?

Thanks for advice in advance.