This can be as creative as you want but at least make the name relevant to what is on you site. E.G. dont have your site name www.penandpaper.com if site is about music.
a good site for you music site would be www.Music4u.com. however you have to have a relevant and good site name that is not taken already . if www.music4u.com is taken, try www.music4u.com.au, it might not be taken.
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 the purpose of the website
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.