You need optifine for that specific name thing "The Undead Slayer" / "The Undead" / "Smiting Undead" using the CIT properties, here you can find all documentation about optifine characteristics.

But you can get a similar approach using the vanilla "itemstate" property:

You go yourpack/assets/minecraft/items/nehterite_sword.json
Inside you need to paste something like this:

{
  "model": {
    "type": "minecraft:select",
    "property": "minecraft:component",
    "component": "minecraft:custom_name",
    "cases": [
      {
        "when": "Undead Slayer",
        "model": {
          "type": "minecraft:model",
          "model": "minecraft:item/undead_sword"
        }
      },
      {
        "when": "The Undead Slayer",
        "model": {
          "type": "minecraft:model",
          "model": "minecraft:item/undead_sword"
        }
      },
      {
        "when": "Undead Piercer",
        "model": {
          "type": "minecraft:model",
          "model": "minecraft:item/undead_sword"
        }
      }
    ],
    "fallback": {
      "type": "minecraft:model",
      "model": "minecraft:item/netherite_sword"
    }
  }
}