Since you aren't using any route values above and instead just the name of the textbox you can just create a link
Name your textbox "name" (if it isn't already) via the html attributes new {id="name"} (for ex)
then you can just jQuery to get the value and append it
<a href="#" onclick="window.location.href='@Url.Action("Edit", "Edit")' + $('#name').val()">Edit</a>
You could also use the html help above and just attach an onclick event handler for jQuery as well.
$(document).ready(function() {
$("#name").click(function() {
window.location.href= $('#idOfLinkHref').attr('href') + '/' + $('#name').val()
});
});
something like that anyways off the top of my head.
There are a lot of ways to do this - these are just a couple ideas.