Right name for frightening experience (9)

I believe the answer is:

nightmare

I'm a little stuck... Click here to teach me more about this clue!

'experience' is the definition.
(I have seen 'Horrifying experience' mean 'nightmare' so perhaps 'experience' could also mean 'nightmare')

'right name for frightening' is the wordplay.
'right name' can be anagrammed to 'NIGHTMARE'.
But, I am not clear how this is indicated.

Can you help me to learn more?

(Other definitions for nightmare that I've seen before include "Frightening dream" , "Terrifying experience" , "dreadful experience" , "Scary fantasy while asleep" , "Bad dream" .)

I've seen this clue in The Irish Independent.

Want a hint initially instead of a full solution? Install my app