Here is the code that shows success in console log but fails when tested with Google's Structured Data Testing Tool or with G+ share button. The original values remain. In this case "jack" never updates to "jill".
var newName= "jill"
$("h1").attr('itemprop','name').html(newName);
Here is the Microdata:
<body itemscope itemtype="http://schema.org/Blog">
<div style="display:none;">
<h1 itemprop="name">jack</h1>
<img itemprop="image" src="http://somehewhere.com/something.png" />
<p itemprop="description">some text</p>
</div>
As you can see, just trying to change the value of "jack" to "jill".