Name Tag

A name tag is an item used to name mobs in the world.

Natural generation
Dungeon chests may contain name tags in stacks of 1.

Fishing
Name tags can be caught from fishing as part of the treasure category. I don't think you can on the Xbox just yet because they just got the update.

Trading
Librarian villagers trade name tags for 20-22 emeralds apiece as part of their tier 6 trades.

Usage
To use a name tag it must first be renamed with an anvil. The player can then it on a mob to give it the name given to the name tag from the anvil. Mobs can be renamed multiple times.

Once a mob is named, they will keep their name, with a few exceptions.
 * A named silverfish that goes into a block will not be named when the block is broken.
 * A named villager will lose its name if it gets turned into a zombie or a witch.
 * A named zombie villager will lose its name if it gets cured.

Limitations
Any mob can be named, except the Ender Dragon and players.

Mobs that can be interacted with by pressing will perform the  action before being named. As a result, adult villagers will open their trading interface instead of receiving the name. Although, the villager will receive the name if he is trading with another player.

Behavior
Renamed mobs will have their name displayed over their head in the fashion as a mob named through a renamed spawn egg. Their names can only be seen if they are aimed at from 7 or fewer blocks away.

Mobs that are named using the name tag will also not despawn in the world, similar to tamed mobs. The only exception is if the mob is hostile and the difficulty is switched to "Peaceful".

If a renamed mob kills a player, the custom name will be used in the death message in place of the mob type name.

Easter eggs
Any mob that receives the name "Dinnerbone" or "Grumm" will be rendered upside down.

Naming a sheep "jeb_" will cause its wool to fade between the dye colors, producing a rainbow effect. This won't affect the wool it drops when sheared or killed.

Naming a rabbit "Toast" will cause it to have a special memorial skin.

Video
Note: This video is outdated, as name tags can now be obtained from both fishing and trading.

Trivia

 * Name tags were added at the request of Paul Soares Jr.