This is a very common question, and the answer is: No. URL ownership and trademark protection are two parallel but very different systems. Owning and using a URL is not enough to protect your name as a trademark, other than providing some Common Law rights through use.
In fact, many founders register or buy a URL -- often for serious money -- and start building their brand around it, only to find out, too late -- after they get sued or receive a cease-and-desist letter -- that they can’t use that name for their planned business, because someone else has prior trademark rights.
It is unwise to spend a lot of (or any) money buying a URL, until you’re sure you can actually use that name as a trademark. (This is just as true, whether you plan to actually register your name as a trademark, or not.)
Before buying a URL, try and get some confidence in the potential to use it for your planned goods or services. Our automated trademark search service here at www.namingmatters.com rates trademark risk in over 30 countries, and is updated daily. Our visualization tool makes it easy to see how crowded your name space is, and instantly judge name risk. Combine Naming Matters trademark availability research with some additional internet searching of your name and goods to check for Common Law use, which can also be a concern in terms of the riskiness of your name selection.