<ul>
<li name="one">1</li>
<li name="two">2</li>
<li name="three">3</li>
<li name="four">4</li>
<li name="five">5</li>
<li name="six">6</li>
</ul>
li
необходимо прописать -onMouseOver={() => this.hover(event.target.getAttribute('name'))}
onMouseOut={() => this.hover(false)}