Edit in JSFiddle

$('.contact-name').hide();
$('#search-criteria').keyup(function(){
    $('.contact-name').hide();
    var txt = $('#search-criteria').val();
    $('.contact-name').each(function(){
       if($(this).text().toUpperCase().indexOf(txt.toUpperCase()) != -1){
           $(this).show();
       }
    });
});

Type something like a , c or x<br><input type="text" id="search-criteria"/>
<div class="contact-name"><h3><a href="##">AABC</a></h3></div>
<div class="contact-name"><h3><a href="##">CACde</a></h3></div>
<div class="contact-name"><h3><a href="##">XYAz</a></h3></div>