This would be called, alters, they are called that because people with dissociative identity disorder have distinct names, memories and voices. Meaning they are alters of their original self.
"In a person diagnosed with dissociative identity disorder, one main "personality" interacts with the world on a regular basis, but other personalities called alters are lurking in the recesses of consciousness."
The anemones are being provided a home and protection, while the boxing crab is using the anemones as gloves to protect herself. In this relationship, both species are being protected which is benefitting both parties. Thus, this is an example of mutualism.