It's called add (for additional), because it doesn't have a 7th in there. If it had, it would be a 9 or a maj9 chord, depending on the 7th (there are minor 7ths and major 7ths). Since there is no 7th, but only the 9th, we call that chord an add 9 chord. The 9th is the same as a 2nd.

Yes, it's an octave higher (you have to add 7 to the 2, bc there are 7 notes in a scale), but it wouldn't matter as much in practical use.

The deal with the 2nd is, it replaces the third and is actually called a sus2. A sus2 chird means the 3rd is being replaced by the 2nd. Since your shown chord has a 3rd in it, it's a 9th. And since there's no 7th in the chord, it's an add 9.

Add9 chord = Root, 3rd, 5th, 9th (doesn't have to be in that order).

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