You were just missing an image tag to change the "src" attribute of:
<html>
<body>
<form>
<input type="text" value="" id="imagename">
<input type="button" onclick="document.getElementById('img1').src = 'http://webpage.com/images/' + document.getElementById('imagename').value +'.png'" value="GO">
<br/>
<img id="img1" src="defaultimage.png" />
</form>
</body>
</html>