Let’s have a hat party.
If you want a hat on your account for something like a project or company association, post here. If it seems legitimate, I’ll private message you and we’ll figure out a way to actually verify your association privately (like receiving an e-mail at a company domain).
These should be things you would need to actually use in the course of posting comments, not just something like maintaining an obscure piece of software that no one will ever discuss or question whether you are actually associated with that project.
It should also be said that just wearing a hat while commenting does not mean you are speaking for that company/project (the usual disclaimer in the comment should suffice), just that it clears up any doubt as to whether you are actually associated with that company/project.
Update 2016-04-06: There is now a formal hat request system that you should use instead of posting here.