Actually I had a conversation with a friend about this, and we agreed to refer to Halo 5 Cortana as Sigma!Cortana, due to her ambition. We realized that Sigma!Cortana is very different to Cortana, Especially in these areas:
Possessiveness. She is very possessive of Chief- even escalating to Yandere levels at times.
Arrogance. She has, with becoming technically immortal had a major ego inflation, nearly as bad as DIO's ego.
Megalomania. Halo 5's Campaign. I rest my case.
And then when I was playing Halo 5 Campaign, I noticed she only called Chief John. The only other person who calls him that is Halsey, who she constantly calls a monster, as a way to justify her actions. But remember as she is a clone of Halsey and they share similar personality traits. Proof of this is when she agreed with Halsey that Chief is "attractive in a primal animal sort of way".
We came up with a theory that stated, and this involves human AIs in general, that rampancy and how it works depends on the individual AIs and their experiences. In Cortana's sake with having the ability to copy herself thanks to her dismantling an Covenant AI, if you remember, in Halo 4, her rampancy was basically a very severe case of schizophrenia. It's possible that Cortana was destroyed when the platform she was in was destroyed and Sigma!Cortana took the reins from then and was deposited into the Domain.
