To a directory site ,it's hard to get traffic from search engine .But my directory has a nice domain name ,"entireweb.biz" which brought some traffic to my site. Many people search "entireweb" and come to my site. So I think good domain name is very important to a directory site.
It definitely helps when the directory name is easy to remember. If they submitted one site earlier, they will go back and submit more when they know the name.
Something catchy is always good from a search engine point of view. Entireweb is a good name, it is also towards the top of the alphabet, which leads into my next point. Also take into consideration submitters. On most directory lists the alphabet is important. Many directories beginning with "A" do very well as they are visited first in submission campaigns. Also since many people give up submitting, or maybe choose only to do a few, the "A"'s tend to do very well traffic wise from the directory lists.
Very useful if you use a dictionary, use unique words. Also use .com domains becasue most users usually type in .com first if they forget the domain.
I suppose this is true for general directories, but for niche it matters a lot less. I think this whole idea of people giving up as they go through the lists is quite significant. It could well mean that you get more quality manual submissions with an A than a Z as the first letter of your domain. For submitters, it's an indication that you may get a better average response time from the Z, Y and X's. Submitting in reverse alphabetical order could be a good strategy for quickly getting links through manual submits.
My directory's domain name was pretty important when I set it up. I wanted people to immediately know what kind of directory it was so that it was clear what kind of sites I was accepting. Although slightly long, it does exactly what it says on the tin...
I believe that it is important to have a brandable recognisable name. A name that people will remember. A few good examples in my opinion are: Joeant, Gimpsy and Umdum.