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

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 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.

There are many important moments in the story, but the most crucial—called "story spotlights"—are shown on cards. These cards have the Planeswalker symbol in their text box; this symbol has no effect on gameplay. You can read more about these events in the official Magic fiction at http://www.mtgstory.com.