One way that you can do that is
1) to turn the weblog title ON so everything is as it should be; and then
2) turn off the DISPLAY of the title. You can do that by commenting out the offending line in the header.php file. The line to look out for, however, is theme dependent. I use Blix and I would comment mine out like that
<!-- <h1> <a href="<?php bloginfo('url'); ?>"><?php bloginfo('name'); ?></a> </h1> -->
If you are not sure, just turn ON the weblog title and then view the page source code. The
<div id=a_css_name"> should give you a good indication of what to look for in the header.php
Is this what you are after?