Testimonial section with HTML tags
I would say that for it to be semantically accurate, the author should be a part of the blockquote, perhaps using a footer.
You should include a cite attribute if the quote has a source.
The quote content should be inside a paragraph element.
I guess now you don't need the wrapper any more.

  &lt;blockquote cite="http://knowyourmeme.com/memes/doge"&gt;
    &lt;p&gt;&amp;ldquo;Such cool. Much awesome. WOW&amp;rdquo;&lt;/p&gt;

     &lt;footer class="author"&gt;
       &amp;ndash; 
       &lt;strong&gt;Doge&lt;/strong&gt;, 
       &lt;a href="#"&gt;The Moon&lt;/a&gt;
     &lt;/footer&gt;
   &lt;/blockquote&gt;

To make it look the same I had to change these bits of CSS:

blockquote {
  font-size: 22px;
  margin: 0;
}

blockquote p {
  background-color: rgb(255, 255, 255);
  border-radius: 6px;
  font-family: Georgia, serif;
  line-height: 1.4;
  padding: 17px;
}

footer.author {
  background-color: transparent;
  font-weight: 500;
  font-size: 22px;
  line-height:22px;
  margin: 24px 0 0 18px;
}

Here's the result.