Find a dungeon, mineshaft, ancient city, woodland mansion, or fishing loot
Open a chest and look for a name tag
Pick up the name tag
Craft an anvil using 3 iron blocks and 4 iron ingots
Place the anvil
Put the name tag in the anvil
Type the name you want
Take the renamed name tag from the anvil
Use the name tag on a mob with an empty hand or by right-clicking it