If a company has the same name as my domain, can I be forced to shut it down?

Check out the domain name section of http://www.wipo.org . There are many cases that you can read through for a more thorough understanding of domain name law.

Whether you will win or not depends on many things including whether you are using your site to steal the company's business, how well known the company's brand is and if it is trademarked, and who owns the trademark to the domain name. If you are serious about keeping your site you should register your domain name with the USPTO (www.uspto.gov) as a trademark.

Oh, and by the way, check out www.cheap-domainregistration.com for $8.75 domain registration.