changing from 1and1 domain name

I installed WordPress 3.0.1 onto my account at 1and1.com. The actual server space is at an ugly URL: s94124006.onlinehome.us, but the URL for my site is https://www.petertevonian.com. When I install WordPress, however, the default WordPress Address (URL) is the ugly s94124006.onlinehome.us, as is the Site Address. Thus, when you rollover one of the posts in the list, the URL that comes up is s94124006.onlinehome.us/category/post-name.

Changing either the WordPress Address or Site Address in the Settings window results in the entire blog not working.

How can I get the links to all use https://www.petertevonian.com as the base URL? I don’t want the ugly s94124006.onlinehome.us showing up anywhere if possible — in permalinks, link URLs, Google results, etc. I’ve read the Permalinks docs, and that seems sort of like what I want, but I haven’t had success yet. All of the “common settings” offered in Permalinks use the same ugly URL. If I ad a custom structure, that’s just being appended to that ugly URL…

Any suggestions or help is much appreciated. Thanks.