MQTT HVAC - Display custom names in UI

I have the following integration working:

climate:
  - platform: mqtt
    name: MySystem
    fan_modes:
      - "0"
      - "1"
      - "2"
      - "3"
      - "4"
    fan_mode_state_topic: "mysystem/fan/raw"
    fan_mode_command_topic: "mysystem/fan/set"

But I dont find out how to give the fan modes names showing up in the UI. As I understand the fan_mode_state_template are the reverse. eg. If the fan_mode_state_topic returns Speed 3, I can convert it to one of the modes specified in fan_modes.

Please advice!