First, from what I can see, your design (data content) for the drop-lists is really weird. Nonetheless, will work with it.
Let's think about how the data is logically linked: the employee number is their common value. Thus, the way you can transfer knowledge between the lists is by using this employee number.
When you select an <option> from a <select> the value of the element is that of the value of the option. Thus, your first list should not use the record number as its value but the employee number (same value for for value= and the visible part. You need to fix this.
Now, the next thing to do is to add an onchange= event to the first list so that when you select a value it will do something with it. You'll need a function for this and possible a good way to do this is:
<select onchange='getName(value)'>
Now your second list can exist as it is except it needs an id= attribute. Let's use the same one as the name= so we'll add
id='e_name' . This is so we can directly access this element on the page. ID's are very important and useful.
Now for your function:
function getName(val) {
document.getElementById('e_name').value = val;
}
That will thus update the second list.
If you load the list when your page is first generated there's no need for AJAX: all the data you need is available on the page.