We often suggest you consider registering a few domain names, depending on what you are wanting to achieve with it.  

If Google Search is a priority for you we would suggest you not only register a domain name that includes your business name but also one that is heavy with your chosen search phrases.  Eg. we have artful.com.au but also some more Google friendly ones too such as managedjoomlahosting.com.au.

We also have the equivalent names with different TLD's. (.com, .net. .net.au etc).  Doing this is more of an insurance policy against anyone else registering them and imitating your business.  Once someone else has them your change of retrieving them are next to none.