(tl;dr) When a moderator closes as a duplicate - if they have a gold badge in the tag(s) they're doing so -- display the gold badge in addition to the diamond
I think it's fair to say that moderators are also active users on their respective site(s) and are most likely "domain knowledge experts" in one or more fields (ie tags) -- and sometimes, yes, when we're not doing our duties as a moderator, we may like to ask questions or answer questions.
"My" site is Stack Overflow - my main tag is "Python" - pretty much all of my "reputation" comes from that tag and I'm honoured that the community has given me the privilege on that tag to "dupehammer" using my gold badge.
What I find a bit uncomfortable is (as a mod) it will put the diamond next to my name which makes it looks a moderator action rather than a "user" action.
I'm not qualified to close-as-a-dupe many things (and I don't unless the community can prove why and hasn't done so already (requires moderator intervention))