What does LOTR प्रशंसकों call themselves, like HP प्रशंसकों are Potterheads?

Ringers, mostly.

I call myself a Tolkienite, but that's because I'm a प्रशंसक of the Hobbit/Silmarillion/Children of Hurin ect/

Good question. Honestly, I don't know if there is one. Ring bearers sounds fine :)

They are called Ringers.
But I like Ring Bearers too :)

Yes, it's Ringers.
But if आप want to make your own name up, that's fine. I've heard different names for different प्रशंसकों of the same fandom. :)

Ringers is the और modern term. untill the two towers sent the lord of the rings into internet-mainstream-land, they were knows oddly as "Lord of the rings Junkies" as if the LOTR was a fix. This was mainly in the era before the films though, but was strongly used द्वारा wetta workshop during production.