I don't really know what to call this piece, but shortly after purchasing my car it fell off on the passenger extreme right side. I suspect the little plastic ledges that 'grab' might be broken as there is very minimal hold when pressed in hard. Maybe there's a trick to it I'm missing, lol.

Does anyone know what this piece is called? I might end up gluing it but would prefer a new one..

 

It looks perfectly OK to me, I can't see any broken or missing bits or tabs.
A few years ago I took these off so I could remove the sun visors to then remove the super annoying "airbag warning" stickers, and they went back on with zero problems. I reckon you should try again to clip it on.

Edit - on closer inspection I can see a missing / broken off tab on the top right of the second pic so you probably need a new one!

 

Hmm, I've tried pushing really hard, angling it in, etc.. doesn't seem to stick.. I'll give it a shot again later. I've done trim removal before but this little piece has me beat, hahaha.

 

Well I managed to halfway clip it from the back by applying a lot of pressure behind the visor, but it still hasn't clipped in all the way. The driver's side was loose on the front and I managed to clip it in 100%, but the passenger side must be somewhat warped as it just won't follow suit.. applying pressure to the front makes the back pop out and vice versa. Tried some pliers with cloth over them, no dice.

 

I had that exact issue the first time I used my driver side sun visor, shortly after picking the car up. I agree it looks as if it should just clip back but it needs to be replaced. My dealer did mine straight away.

 

To answer your original question, it' s called a Sun Visor Cover. Right side looks to be part # C2Z12631PVJ Check with your dealer.

 

Thank you. I'll ask the dealer what they can do about it.