Chapter 9 endnote 36, from Lisa Feldman Barrett.
Some context is:
you can think of this repertoire [i.e., multiple selves] as instances of a single, goal-based concept called “The Self ” in which the goal shifts based on context. [...] Could it be that the population of instances which are “your self ” are held together by a word — perhaps your name?
Here's a fanciful musing: In an emotion category such as “Fear,” the instances are diverse enough that no objective criteria in the body or face are required to hold the category together. I wrote in chapter 5 that the concept’s name—the word "fear" or its synonyms—may be the strongest statistical regularity among all its instances. Well, if the category “The Self” also has wildly diverse instances (child, student, friend, lover, cook, etc.), might the same reasoning apply? How is it that instances of yourself as an infant, a young child, an adolescent, a middle-aged adult, and an older adult can all be you? Perhaps one powerful element holding these diverse instances together is your name. After all, you’ve had a lifetime of statistical learning in which you and other people have paired your name with sensations from your body and the world, giving you plenty of opportunity to bootstrap a concept of the self. No essence is required: a dynamic, goal-based concept will do fine.
I wouldn’t take this idea too literally. A person can change names without changing identity. But it might explain why people are attached to their own names and are reluctant to change them.