You should not put your logo or website title in an h1 tag, the page title should be what is in the h1. The h1 defines the title of the page and the content on it, not the title of the website, that is what the <title> tag is for.
From an SEO perspective it is one of the first things crawlers look at and one of the main items Search Engines use to categorize and rate websites, having the same h1 tag on all of your pages (e.g. the name of the website) is going to heavily negatively affect this, because generally crawlers only read the first h1 tag.
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