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 protectible brand that adds value to your business depends on what you choose, so choose wisely.
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 protectible 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.
If you are going to invest money into creating and promoting a website, you should adequately protect the domain name as a trademark. It is insufficient to simply secure a domain name registration and in some cases can be fatal. One of my clients was sued by Amazon over his use of amazonnetworks.com for computer services. He innocently registered the domain and put up his site with a picture of the Amazon River. At about the same time, Amazon.com established its site and was selling only books. Because he failed to "stake out his claim" to the term for computer services by securing a federal trademark, Amazon turned into a trademark bully and sued him 10 years later. He was forced to sell for a fraction of what it was worth, as he could not afford to fight the lawsuit.
Once you have a term in a domain that qualifies as a trademark, the key requirement is that you offer goods and services for sale, not merely provide an "informational" site.
An informational site describes you and what you do or sell, but does not actually deliver services or products online. For example, an attorney was refused registration of http://www.eilberg.com/ because the site merely showcased his services.
If you provide services online through your site, the Trademark Office will grant registration. For example, the ability to sign up for courses or workshops online is a service.
Other examples of registerable websites include online banking services, online chat rooms, online retail services, real estate marketing services with virtual tours, and hosting web sites of others.
It is up to you to decide. I believe if one is going to spend the money to market and promote goods and services online, it is wise to have a term that can be protected as a trademark as well as a domain. Whatever you decide, choose based upon an understanding of the difference between the two.