As the name implies, a trademark is for protecting a business or trader. You could trademark a company name, and if others used the name online you might have some protection.

Is there a particular reason you want to 'protect' the name?

Trademarks are not an absolute protection. If you trademarked BrooklynBlue, as, say, the name of an online store specializing in blues records created by Brooklyn artists, then you would not be able to stop someone living in Brooklyn who painted blue paintings from using the nickname "BrooklynBlue" in an online forum for artists.

Material that you post in online forums and such will be subject to their terms and conditions. Many say that material is copyright of the contributor. In that case, you have copyright from the moment you write it--as is the case for anything you write anywhere. Other people do NOT have the right to copy it. Registering it at the copyright office just gives you specific additional legal rights.

From your post, you seem to need to learn some basics about copyright and trademark law, and I'd suggest you read up in the FAQs at the copyright office and at resources such as this: [fairuse.stanford.edu...]