For authors, I feel that this question is not as important as it for a traditional business.
A custom domain name does suggest a bigger commitment to branding but also comes with a slightly larger technical commitment. That’s why Author Buzz UK offers free blogs – when you make your group you can have a blog set up for you pretty much instantly.
If you know what you are doing enough to set up your own hosting and domain name, this is certainly an attractive option – custom email address, less text on your business card, your-name.com, and slightly better SEO. However, if that seems like too much, a free yourname.authorbuzz.co.uk type name is just as good.