This depends upon the nature of your question. When it comes to the domain checker, you don’t need to add www in front of the domains that you search for.
When it comes to how you stylise your URL once you’ve bought it, it comes down to personal choice, although whichever you go with, you should make sure that it’s always consistent. If your website resolves at both http://www.yourname.com and http://yourname.com, it’s effectively treated as two different websites.
Historically, websites included www in front of the domain so that when their URLs were included on packaging, posters and other offline marketing materials, people knew that it was a ‘World Wide Web’ address. Nowadays, though, the internet is so ubiquitous that it’s no longer really necessary to include the www, and many people argue that removing it makes it easier for people to remember web addresses.
