You may register any domain name you want, up to a point. Your domain name must be unique because it is an address that can point only to your web site. Additionally, you cannot register a domain name that is trademarked by another company or is so similar to a trademark that it is confusing or easily mistaken for the trademark. Recent disputes with ICANN have made it clear that a domain name registered in bad faith or with no legitimate interests in the domain name will result in a dispute.
