Answer
As mentioned by @Ategon@programming.dev, if only a username is shown, then that is the display name that the user has set. If there is a username and an instance, then that user has not set a display name.
Original Post
There appears to be no rhyme, nor reason to the inclusion of the instance in the poster’s username. For clarity, I am referring to the format of @username@instance. I would have thought that the usernames that don’t include the instance are from users that originate from one’s local instance, but that appears not to be the case. The second idea was that maybe it was something to do with length, in that a longer username wouldn’t include the instance, but that doesn’t seem to be the case either.
I think it should always display as without instance if it’s a local post on the same instance, and with instance if it’s a remote instance. That would make sense. But unfortunately the display name being configurable confuses things.
I could probably set my display name to be 1984@lemmy.ml without having an account there even.