In XBox 360 edition, name tags are a new addition. Currently the only way to get them is dungeon chests. However many people have pre-explored worlds and therefore name tags won't generate. Due to Creative banning achievements, there is no way of getting these in old worlds without such. However i have the solution: Crafting!
Name tags are crafted like a lead, but with Iron instead of Slimeballs.
Name Tags should be offered as a Tier 6 Librarian trade item in a future update... but I support crafting for saddles and name tags in general. Name tags were first tradable in 1.8, probably will be brought forward next update. We'll probably also getting the chance to fish them in the next update, because that was added in 1.7. Still, it would be good to be renewable by crafting.