Re: Where to set the meta tag or website name exactly?
Since you are seeing the text "Site logo" in the search results, I assume you need to replace the default text associated with your site logo, which is on the Look and Feel admin page. There are two text fields related to the logo: "Logo title (on mouse over)" and "Alt. description (e.g. for text browsers)". These can be changed to match your site identity.
-- Gary