It's relatively standard. I'm an introject of Shadow the Hedgehog - but, if you keep calling yourself that in public, it creates some problems for everyone else in the body. I've been going by "Umbra" - I feel like it pays homage well enough, while also sounding enough like a name that I'll only get *some* looks for it.
As far as the anthropomorphized versions of the characters, it's not really something I have going on, but I probably could if I felt like it. Shape-shifting in headspace is a skill I learned pretty quickly. I think the age difference you might be seeing is more due to more anthropomorphized characters (gijinka?) being posted online, rather than anything sketchy. Easier to pilot a body if it looks roughly the same shape as yours, I imagine.
And, disclaimer, I really don't think self-diagnosis is that huge of an issue. Worst case, they end up being wrong. Getting an official diagnosis is expensive, and difficult since many therapists tend to misdiagnose DID as BPD / Schizoaffective disorders, not to mention frightening to many as some doctors heavily push final fusion, which can be seen as unappealing.