Joel Spolsky has a fantastic post on community identity that every business should read.
Should we have dogs.stackexchange.com and cats.stackexchange.com? Or PoochQAndA.com and KittyQueries.com? If everything lives at stackexchange.com, the brand carries across all the sites. So if you had a great experience with motorcycles.stackexchange.com, you might believe that chess.stackexchange.com a good chess site.
[…] we decided that individually-branded sites felt more authentic and trustworthy. We thought that letting every Stack Exchange site have its own domain name, visual identity, logo, and brand would help the community feel more coherent. After all, nobody wants to say that they live in Housing Block 2938TC.
Many businesses listen to their web team and put the community as a sub domain of the website. Some don’t even bother to name it at all. It just exists as community.domainname.com. These communities don’t do well.
The better community businesses pick a name using insider jargon [Thanks Joel] that reflects the community itself. They let the community develop an identity that might be unique from the website itself.
Just because it’s easier to host it on your own domain, doesn’t mean you should.