No, owning a URL is not enough to protect your name as a trademark, other than providing some Common law rights (see FAQ on Common Law).
It is probably unwise to spend a lot of money buying a URL, until you are sure you can actually use that name as a trademark, whether you plan to register it or not. For maximum protection, a Federal trademark grants you important rights in the United States to use and defend your name, for the goods or services you have described.
This means that if others attempt to use your name for similar goods, or a name that is similar to your name for similar goods, you have legal remedies to object to their use and potentially stop them.
You can also obtain trademark rights in additional countries by filing in those countries.