No, thank you. Even if you can find one (most of them seem to have been registered already, by people who didn't ask whether we actually wanted it before they applied), we're happy with the PuTTY web site being exactly where it is. It's not hard to find (just type ‘putty’ into google.com and we're the first link returned), and we don't believe the administrative hassle of moving the site would be worth the benefit.
In addition, if we did want a custom domain name, we would want to run it ourselves, so we knew for certain that it would continue to point where we wanted it, and wouldn't suddenly change or do strange things. Having it registered for us by a third party who we don't even know is not the best way to achieve this.