Issue:
Saddles lose their name after 'using' it on a horse.

Steps to reproduce:

1. Name a saddle using an anvil.
2. Right-click on a horse to equip the saddle.
3. Remove the saddle from the horse's inventory.
4. The name has been removed from the saddle.

Expected behavior:

When mobs pick up dropped items, such as a zombie picking up a sword, the items keep all their information (name, enchantments, etc).  I expected my saddle to retain its name after equipping it to a horse.

During the early game, when nametags had not yet been acquired, I tried naming saddles so I could check the horse's inventory and look at the name of the saddle to help me tell the horses apart.  If I open the horse's inventory and manually place the saddle on the horse, the saddle keeps its name.  However, if I right-click on the horse with the saddle in my hand it immediately puts a (generic) saddle on the horse and removes the named saddle from my inventory. 

Using a saddle on a pig or strider has the same result, they drop a generic un-named saddle upon death.  I suppose that is to be expected for pigs and striders as they don't necessarily have an "inventory", but rather a true/false value for their saddled property.  However, I know that the inventory of the horse CAN hold a named saddle because it works when placing the saddle on the horse manually.  So, I believe that 'using' of a saddle on the horse should work the same way (have the same effect) as placing it on thru the inventory interface, allowing it to keep its data.

Right-clicking a mule or donkey with a saddle in your hand does NOT automatically equip the saddle, so this cannot be replicated for those animals.