Depends on the purpose of the website
A good website name generator would depend on what the name was being used for. The website known as Impossibility is reputed to be good for generating domain names. Alternatively if a baby name is desired then a good website would be babynamegenie.
Depends on what type of website Depends on what type of website
Here's a link to a good name-generating website that can help you out.
Here is a link to a good name generator website
babynames.com
Here's a good link to a last-name generating website.
Here's a link to a good name generating website.
There are many different names that would be good for a chat website. You could call your website Chatter Channel for example.
Twitter...
I'm not sure what a "fight name" is but here's a good name generator website.
Here's a link to a good online name generating website for you.
Perezhilton.com Celegossip.com