The notes to build an arpeggio are 1,3,5,8. You can just build one with 1,3,5. But I always add the Octave. You can use any combination to build an arpeggio though, arpeggio just means "broken chord", you could double the fith an cotave higher. Your best to use 1,3,5 though as this determines whether it's minor, major, diminished, augmented etc.

The actual names used for scale degrees are:

1 = Tonic
2 = Supertonic
3 = Mediant
4 = Sub Dominant
5 = Dominant
6 = Sub Mediant
7 = Leading note
8 = Tonic (Octave)

I usually just say:
1 = First or Root
3 = Third
5 = Fith
8 = Octave

So to put it simply, you can call the third note in a scale the mediant or third, it's up to you. Same goes for any of the others.

Hope this helps...

- J