Once you register a domain name, others cannot use it as their web address. A domain is a lot like a street address or location on the Internet.
However, this does not automatically mean you can register it as a trademark protected by the federal government for your products and services. Whether it can also function as a legally protectable brand that adds value to your business depends on what you choose, so choose wisely.
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The answer often depends upon whether you have chosen to market your products or services under a generic or highly descriptive domain. Generic and descriptive terms are not normally protectable as a trademark.
A great example is hotels.com which spent a fortune in 2007-2008 trying to convince the Trademark Trial and Appeal Board and Federal Circuit that it has acquired "secondary meaning" in the domain. They failed because no matter how much they promote or market the term, it will still be generic for what the consumer finds at the site.
On the other hand, valuable brands on the Internet are not generic and descriptive. A domain such as EXPEDIA.COM is registered and protected as a strong trademark because the owner actually provides services through the website.
EXPEDIA may suggest but does not describe what is being offered at the site. Google, eBay, and Amazon are all domains turned famous trademarks because their owners not only registered the term as a domain but chose a term that could also be distinctive for trademark purposes.