I am traumogenic (trauma created/clinical DID) plural system. It is highly likely that I never had a "core personality" that I was born as and instead have always had either an infant mental state or multiple personalities. (During the time most babies begin to form a coherent personality, I formed several. It is possible that not every system forms like this but highly like I did)
Every time I've felt I was singular, I've experienced mental walls, amnesia and other DID symptoms. If someone could do a "I'm singular ama" that'd be cool because I have questions too. :)
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Some gives names and some don't. Some systems may be reluctant to share names because the names may be directly linked to a trauma and other systems advocate strongly for people to use the names of their system members. How the alters in my system got their names is a good question. I had thought that I may have named them but the more I increase communication and decrease amnesiac barriers, the more I see how that notion was likely clinical grade "host"/front person not understanding things.
Like, I thought I named one alter after a parody song that they kept referencing to show how badass they thought they were. "Okay fine, you want to keep playing the X song? You can be X now!" Which I thought was kinda funny but then I realized that this alter may have already claimed that name and were using song to communicate that or maybe the name did stick from a song. Either way, they respond to that name now so it works.