If it's truly just styling that needs to change, then you don't need JavaScript at all. You can just use CSS with the :hover
pseudo-class:
.normal { background-color:#e0e0e0; }
.normal:hover { background-color:yellow; }
<nav id="frame-link">
<a href="index.html" name="home" class="normal">Home</a>
</nav>
But, if it's more than just styling, then you'll want to do this the modern, standards-based way. Don't use inline HTML event handling attributes (see here for why). This syntax is a little more typing, but well worth it for all the benefits it brings.
Lastly, (and again), if it is styles that you're after, working with classes is much simpler than working with individual style properties.
// Get a reference to the element that needs to be worked with
var theLink = document.querySelector("a[name='home']");
// "Wire" the element's events
theLink.addEventListener("mouseover", mouseOver);
theLink.addEventListener("mouseout", mouseOut);
function mouseOver() {
theLink.classList.add("hovered");
}
function mouseOut() {
theLink.classList.remove("hovered");
}
.normal { background-color: #e0e0e0; }
.hovered { background-color: yellow; }
<nav id="frame-link">
<a href="index.html" name="home" class="normal">Home</a>
</nav>