Template button name

Configuration
1

Hello,

I have the next code to create a template button:

template:
  - button:
    - unique_id: 'start_stop_stopwatch'
      name: >-
        {% if is_state('input_boolean.start_stopwatch','off') %}
          {% if is_state('sensor.stopwatch','00:00:00') %}
            Start
          {% else %}
            Resume
          {% endif %}
        {% else %}
          Stop/Pause
        {% endif %}
      icon: >-
        {% if states('input_boolean.start_stopwatch') == 'off' %}
          mdi:play-circle-outline
        {% else %}
          mdi:stop-circle-outline
        {% endif %}
      press:
        service: input_boolean.toggle
        target:
          entity_id: input_boolean.start_stopwatch

This code creates an entity called button.start (Start is the initial name given to the button in the template).

My question is: Why the entity is not called button.start_stop_stopwatch?

If I want to create a second button with a different unique_id but with same name template, I don’t see it created, or maybe HA creates the same button twice. How can do it?

Thank you.