Ixalan's Binding has this text:
When Ixalan's Binding enters the battlefield, exile target nonland permanent an opponent controls until Ixalan's Binding leaves the battlefield.
Your opponents can't cast spells with the same name as the exiled card.
God Eternals, such as God-Eternal Oketra, have this line:
When God-Eternal Oketra dies or is put into exile from the battlefield, you may put it into its owner's library third from the top.
If I target God-Eternal Oketra with Ixalan's Binding, and the opponent chooses to put it back into his library 3rd from the top, will he be able to cast the God-Eternal without destroying Ixalan's Binding? That is, does Ixalan's Binding "remember" the name of the card that was exiled before it was put back into the deck?
If the answer is yes, the opponent can recast the God-Eternal, does that mean that if the exiled card leaves exile for whatever reason (e.g. it was processed by Wasteland Strangler) then Ixalan's Binding second effect ceases to work?