I want to remove the site name that is under the toolbar because the logo is already in the toolbar. I can't find where to change this. 
My site is www.kasias.nl 
Can somebody please help me ?

To change your page name go to /Yoursite/templates/mobile_iphone/index.php

Adjust this row
<h1><?php /** @var JSite $app */ $app =& JFactory::getApplication(); echo $app->getCfg('sitename'); ?></h1>
Delete the php stuff or Insert a image, or write your own Title.

I see that your "back" and "Home" buttons are still blue, while your toolbar color is black.

Try this Photoshop file!
Here you can cange color and gradients to the buttons and cut them out and export them to your site.
The buttons for Iphone is availebel here:
/yourSite/templates/mobile_iphone/jqtouch-src/themes/apple/img/
replace them, but with the same name.

The file is made in adjustable Vector format (no pxels, when rezising)

http://www.teehanlax.com/blog/iphone-4-gui-psd-retina-display/

www.teehanlax.com/blog/iphone-4-gui-psd-retina-display/

You might want to remove the bar as well as the title copy.

Remove '<div class="toolbar">
<h1><?php
$app =& JFactory::getApplication();
echo htmlspecialchars_decode($app->getCfg('sitename'));
?></h1>' - lines 45-49
+ remove
'</div>' - line 54

This worked for me