Minecraft wiki entry for Item_modifier, associated text: set_name—Adds or changes the item's custom name.
 name: A JSON text component, overwriting the previous custom name on the item. Components requiring resolution are resolved only if entity successfully targets an entity.
 entity: Specifies the entity to act as @s when referenced in the JSON text component. Set to this to use the entity that triggered the item modifier, killer for the entity that killed the this entity, or killer_player to target the killer only if they are a player.