If the owner is skilled in promoting and advertising then they can get their users to promote the new name, also adding a .htaccess coding to redirect the old domain to the new one.
I ran a forum called Forum Advertizer and after a while I changed the 'z' to an 's' in the word advertizer (because the domain came available).. Didnt hurt anything at all.
However thats just a minor change.
It could affect buisness though. Comparing to the real world: a chain of pharmacy / department stores around here called "Longs" were recently bought out by "CVS" and all the names of the stores changed. Several people switched their prescriptions to Wal-Greens or Rite Aide, which are more well known and established pharmacy/department stores. CVS is new and unknown to the west coast. They should have just kept the name and they wouldnt have lost out on tons of buisness.
All and all I guess its a gamble. Could work in your favor or not.
I can say it definitely does change things. I changed the name/domain of my site back in January and it's definitely affected the site. However i had to change it because the whole concept of my site changed and the name never suited it anymore, although the old domain still redirects.
But changing the name is not really a decision that should be made lightly.
UW started as Nukia. This is because the first country, still today owned by me, was called "Nukia." The root ZB URL remains Nukia to this day.
Pretty much explains it. If you need to change it, leave the old URL there. That way your old members go to that URL and just see that the name has changed. What I do not like, however, is when you simply close the forum and reopen it somewhere else, or delete altogether, then rebuild on another site. You shouldn't go changing name frequently, though. Maybe once in the life of your forum.
I wouldn't change a name of a forum unless I'd thought of a really good name and the current one is crap. Changing names can confuse people and forums it can be really hard to change.