This doesn't sound logical because you should be the person who owns the domain, not them.
For hosting, I recommend:
Host Gator is by far the best in my opinion to start out for you. I think they are better than Yahoo! I already host 5 websites with HostGator and seriously, web site hosting and management can't be any better!
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# cPanel Hosting (totally awesome features!)
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Plus if you were switching from another host:
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They also have over 4,500 web templates when you sign up!
They have a 45 day money back guarantee
They have energy friendly servers!
24/7 support tech.
Plus they've won many awards!
You can go through the affiliate on my website to benefit us both if you want. Just scroll down on the page and click on one of the HostGator link banners.
http://www.armengrecotech.com/page6.php
Good luck, and I hope I helped!
If you have anymore questions, feel free to contact me! I'll surely help you out!
:)