But I am not even sure if this is correct. And the details eludes me. For example: How do I discover what name to include in myservice.services.yml?
Now that Drupal 9 is end of life you no longer need to do that. Replace the argument list with the autowire option:
mymodule.services.yml
services:
mymodule.my_service:
class: Drupal\mymodule\MyService
autowire: true
See the change record: Core services provide aliases for autowiring