Pollen-Shield Hare // Hare Raising

If an adventurer card ends up in exile for any other reason than by exiling itself while resolving, it won't give you permission to cast it as a permanent spell.

If an effect instructs you to choose a card name, you may choose the alternative Adventure name. Consider only the alternative characteristics to determine whether that is an appropriate name to choose.

If an object becomes a copy of an object that has an Adventure, the copy also has an Adventure. If it changes zones, it will either cease to exist (if it's a token) or cease to be a copy (if it's a nontoken permanent), and so you won't be able to cast it as an Adventure.