In psychiatry and psychology, there is no such term as "split personality." My patients and their families in the past used to hear the term "split with reality" when named as an element of schizophrenia and immediately went to "split personality" as their term of choice instead.
Many people split off or away from reality now and again, but usually what a person using the term "split personality" means is dual personality or multiple personality, as was used most often in the 1970s - 1980s for the current diagnosis of Dissociative Identity Disorder.
We had one woman patient that had two personalities and each worked a separate full time job for quite a while. Each personality wondered why she was so tired. Having two bedrooms and closets containing two different wardrobes, each personality assumed that the other was out working. They left notes for each other. She did reintegrate and was surprised that she could continue working 80 hours a week for so long.