I’m the admin and moderator at discourse.biologos.org, a popular discussion site about faith and science connected to www.biologos.org. I was wondering whether there’s any legal issues with the site title using the word “Discourse”, and us referring to the page informally as the “Discourse” page. What sort of attribution should we use to make sure people know the Discourse engine isn’t our own creation?
Well, discourse is an English word that you could use where you want I suppose.
Yes, using discourse.example.com is perfectly valid.
From a “usability” point-of-view (or SEO) I would vote against naming something after the technology it uses.
Instead I would use a term that expresses the content/intention of the website.
E.g. our community-URL is named “community.zeta-producer.com”.
So I would recommend to give the user and Google better information about what content he can expect on that domain, not what technology.