If you have Demonic Demise Dragon, Azi Dahaka as your buddy, you may buddy call using this card. If so, you call Demonic Demise Dragon, Azi Dahaka from your buddy zone by paying the call cost (both costs are the same, so it doesn't matter which gets paid) and put this card to the buddy zone at rest.
This situation also works when the cards are switched with Yearning as the buddy and Demonic Demise is being used to buddy call (in this case, Yearner is called).
It works like this because this is treated as having the same name as Demonic Demise, no matter where it is.
You can have 4 of each version in your deck, as the "you may only have up to 4 copies of the same card" rule only applies to the name printed on the card itself and not any names it may also have via effects.