You may choose the name of a land card. Cards with that name can still be played (since lands are never cast), but damage they would deal to you and your permanents will be prevented.

If you choose the name of a split card, you choose one name, not both. For example, you could name Failure or Comply, but not Failure // Comply. Opponents are still allowed to cast the half you didn't choose.

You must choose the name of a card, not the name of a token. For example, you can't choose "Zombie" or "Ragavan." However, if a token happens to have the same name as a card (such as an embalmed creature token), you can choose it.

There are many important moments in the story, but the most crucial—called "story spotlights"—are shown on cards. You can read more about these events in the official Magic fiction at http://www.mtgstory.com.