how to use get_field_name in external ajax handler

Question

Why you want to use ajax for showing some fields on form in widget?
Can’t it be done using simple show hide using jquery. See below. Not tested , just to give insight.

HTML

<input type="radio" id="someradio" />
<div id="somediv" style="display:none;">
    <input type="text" name="<?php $this->get_field_name('name'); ?>">
</div>

Jquery

<script type="application/javascript">
    jQuery('#someradio').on('click',function(){
        jQuery('#somediv').toggle();
    });
</script>