What should I name my website ?

[Jake]

It can cost a bit of branding promotion expense it you use a simple descriptive name that describes the function of the site, which search engines can identify, rather than some vanity name. Some niche sites are able to use an exact search phrase people use in searches as a site name, giving it a measurable advantage in search ranking.
In the past some successful people have ended up selling businesses with their name, leaving them less options for the next business.

There are sites with tools that help you come up with fictitious names, including: wordlab.com, naming.net, wordoid.com, lingzini.com, namestation.com, some of these tools look up the domain name availability as you go.
Any name not already used in a .com web site name is probably not trademarked.