The Triune brain model suggests our brains evolved adding more layers, a lizard brain, then a mammal brain, then a new human brain. As that's false, and the same structures have become modified in different ways in different lineages, what is the name of this current model?
There isn’t a new model, exactly, since as the poster stated, the brain doesn’t operate as a model and earlier versions of brain structures simply modify themselves to evolve— it’s one brain. Meaning, one’s “lizard brain” is actually just a mammalian brain now. The new model perhaps is The Human Brain? But given that the Triune model was most popularized by lawyers needing it for defense against emotional (irrational) behavior and psychologists adopted it for explanation of emotional dysregulation, then likely the best replacement is theory about emotion. Emotions are not well understood, and there are several theories about them, but the latest and most provocative development is the Theory of Constructed Emotion. See Barrett-Feldman et al.