Which HTML5 tag should I use to mark up an author’s name?

Both rel="author" and <address> are designed for this exact purpose. Both are supported in HTML5. The spec tells us that rel="author" can be used on <link> <a>, and <area> elements. Google also recommends its usage. Combining use of <address> and rel="author" seems optimal. HTML5 best affords wrapping <article> headlines and bylines info in a <header> like so:

<article>
    <header>
        <h1 class="headline">Headline</h1>
        <div class="byline">
            <address class="author">By <a rel="author" href="https://stackoverflow.com/author/john-doe">John Doe</a></address> 
            on <time pubdate datetime="2011-08-28" title="August 28th, 2011">8/28/11</time>
        </div>
    </header>

    <div class="article-content">
    ...
    </div>
</article>

• The pubdate attribute indicates that that is the published date.

• The title attributes are optional flyovers.

• The byline info can alternatively be wrapped in a <footer> within an <article>

If you want to add the hcard microformat, then I would do so like this:

<article>
    <header>
        <h1 class="headline">Headline</h1>
        <div class="byline vcard">
            <address class="author">By <a rel="author" class="url fn n" href="https://stackoverflow.com/author/john-doe">John Doe</a></address> 
            on <time pubdate datetime="2011-08-28" title="August 28th, 2011">on 8/28/11</time>
        </div>
    </header>

    <div class="article-content">
    ...
    </div>
</article>