You can do that just using CSS.
You'll need to place another tag inside the <a> and then you can change the CSS background-image attribute on a:hover.
i.e.
HTML:
<a href="#" id="name">
  <span> </span> 
</a>
CSS:
a#name span{
  background-image:url(image/path);
}
a#name:hover span{
  background-image:url(another/image/path);
}
Try something like this:
HTML:
<img src='/folder/image1.jpg' id='imageid'/>
jQuery: 
$('#imageid').hover(function() {
  $(this).attr('src', '/folder/image2.jpg');
}, function() {
  $(this).attr('src', '/folder/image1.jpg');
});
EDIT: (After OP HTML posted)
HTML:
<a href="#" id="name">
    <img title="Hello" src="/ico/view.png"/>
</a>
jQuery:
$('#name img').hover(function() {
  $(this).attr('src', '/ico/view1.png');
}, function() {
  $(this).attr('src', '/ico/view.png');
});
jQuery has .mouseover() and .html(). You can tie the mouseover event to a function:
The same thing can be done when you get the mouseover event indicating that the cursor is no longer hanging over the div.
I know someone answered this the same way, but I made my own research, and I wrote this before to see that answer. So: I was looking for something simple with inline JavaScript, with just on the img, without "wrapping" it into the a tag (so instead of the document.MyImage, I used this.src)
<img 
onMouseOver="this.src='ico/view.hover.png';" 
onMouseOut="this.src='ico/view.png';" 
src="ico/view.png" alt="hover effect" />
It works on all currently updated browsers; IE 11 (and I also tested it in the Developer Tools of IE from IE5 and above), Chrome, Firefox, Opera, Edge.
Thy to put a dot or two before the /
('src','./ico/view.hover.png')"
here's a native javascript inline code to change image onmouseover & onmouseout:
<a href="#" id="name">
    <img title="Hello" src="/ico/view.png" onmouseover="this.src='/ico/view.hover.png'" onmouseout="this.src='/ico/view.png'" />
</a>