varnava,
<div class="taxonomy-images">
<a class="taxonomy-image-links" href="/artists/andrey">
Andrey
</a></div>
<script>
var a = document.getElementsByClassName("taxonomy-image-links")[0];
var div = document.createElement("div");
div.className = "name";
//или div.setAttribute("class", "name");
div.appendChild(document.createTextNode(a.innerHTML));
a.innerHTML = "";
a.appendChild(div);
alert(document.getElementsByClassName("taxonomy-images")[0].innerHTML);
</script>