I'm not using Damus, but I'd presume there's a way to edit your "nostr profile" or "about you" kind of area. there should be an area for a "NIP-05" or maybe "nostr address" if it is not called that.
I haven't used the nostr check service, but I'd presume you gave them your pubkey as well as a display name of your choice.
in the nip-05 field in your profile, you'll add the name you gave them, "Rubainski@nostrcheck.me", or whichever "@" address they gave you/you signed up for.