All player moderators have a silver crown next to their name in your text window. Jagex moderators will have a gold crown and the word 'Mod' at the start of their name, whilst local moderators will have a purple crown. Anyone claiming to be a moderator who doesn't have these accreditations should be reported for staff impersonation.
The name you have mentioned is clearly misconceiving, and you should take the time to report this incident to email@example.com.
Remember, you will only be contacted to become a moderator through your messaging centre, and not through Private Messages in-game.