Personal identity has an established place in the philosophical universe but personality is not so sedulously studied. People have personalities (some animals too) but not much is said about them by philosophers (by psychologists, yes, where personality theory is part of the curriculum). Why not? There are some good philosophical issues here, and the subject is certainly of considerable intrinsic interest (and not just to philosophers). There is first the question of the ontological status of personality traits: what are these exactly? A psychologist will tell you about the Big Five personality traits–openness, conscientiousness, extroversion, agreeableness, and neuroticism—and you will have some idea of what she is talking about; but it is not so easy to say what having these traits consists in. The philosopher might lazily announce that such traits are dispositions to behavior without inquiring too closely into what precisely such a disposition might be, both with respect to its intrinsic nature and the range of behavior held to characterize the disposition. Is there any more reason to be a behaviorist about personality than any other psychological fact? The problem, evidently, is that personality traits are clearly not reducible to experiences or beliefs or speech or episodes of behavior, and yet they are perfectly real things. There may well be associated qualia and conduct, but these are not what such a trait is. The trait itself seems curiously elusive, being neither observable from the outside nor introspectable from the inside. It is perhaps the basis of a set of dispositions, which may be very various, but it is not simply identical to such a set—any more than molecular structure is identical with its associated dispositions. So there is first of all a fundamental question of ontology, with the usual threats of reduction, elimination, and mystery. We don’t have any clear idea of what a personality trait is.
Other questions quickly crowd in. Is there something it’s like to have a certain personality trait, say extroversion, or is personality phenomenologically blank? Is personality a causal factor in the production of behavior, in addition to belief and desire and other recognized factors? Is it part of the explanation of intentional action? Does it cause action? How does personality relate to the brain? Could it be identical to a brain state? If not, why not (it has neither semantic content nor qualitative character)? Are traits of personality analyzable in any way: do they have compositionality or hidden structure? Are they definable? How are they related to desires? Certain desires seem characteristic of a given trait, but is there any necessary relation? Do extroverts always and necessarily desire to hang out with other people? What causes such traits to exist in an individual—genes, social interactions, education, reading habits? And what causes them to change and possibly disappear? How plastic are they? Can there be a complete alteration of personality? Traits don’t come and go like sensations or beliefs, but they do seem to be in a constant state of flux; they are not just passive elements of one’s psychological anatomy. They grow with age and can become atrophied. Are they supervenient on other parts of the psyche, particularly desires; or are desires supervenient on them? How exactly do personality traits interact with desires? Do they sometimes fix beliefs? These are all good questions, but we don’t find philosophers addressing them. It’s as if personality doesn’t exist so far as the philosophy of mind is concerned. 
Personalities notoriously vary, but are there any personality universals? Are there personality traits that all humans share? Is there a species personality? This question is like the corresponding question about languages; indeed, there is quite an exact parallel. Despite many local variations there is a substantial core of common traits—a human type. The same is true for other species, as any pet owner knows. Humans are apt to be acquisitive, competitive, social, family-oriented, hospitable, nervous, and afraid of death (among other things)—though there is much scope for variations of expression and different triggering conditions. No doubt this phenotypic coincidence has a genetic basis: we humans are born with a specific type of personality different from the personality of big cats and tortoises (say). Do humans always have a personality? There may be pathological cases, such as brain damage, and we have all heard the phrase “he has no personality”, but any normal human has one—though it may not be scintillating or agreeable. A personality is your birthright, for good or ill; you have no choice in the matter. You have one as surely as you have a body or brain. You might be able to have it removed, but then you will end up like the proverbial vegetable. You exist; therefore you have a personality. Indeed, you exist as a personality: that is what you essentially are. What makes me me is my personality more than anything else: take that from me and you rob me of my essence. You can take my memories, all of them, and leave me intact as long as my personality survives. If I have many personalities, you might be able to take some of them and leave me still on the premises; but if I am rendered a personality vacuum, I am effectively extinguished.
How limiting is personality? Is it like having a limit to memory? Does your personality prevent you from achieving certain things? Is it possible to transcend one’s personality? We are certainly not free of our personalities (single or multiple), but is it possible to bracket them, to break free of them? The question is not easy: don’t we need another personality in order to break free of this one, or can we step into a personality void and proceed from there? Is there such a thing as personality-independent action? Some have thought that God can confer such an ability (think of Saul on the road to Damascus), but doesn’t there need to be some personality germ in there that makes such a thing possible? How can I just lever a brand new personality into being? Don’t I need a personality to do that, and mustn’t this personality somehow carry the new one within it? I can’t make myself be a patient person, say, simply by willing it (though I might be able to moderate my impatient actions). Aren’t we really imprisoned by our personalities? Don’t our personality traits form the bars of our existential cage? Don’t they sharply limit our freedom? At best you can use one trait to do battle with another (Agreeableness versus Impatience), but you can’t set yourself against your entire personality. Personality is fate. What personality is exactly is not so clear, but it is clear that it has a powerful grip on us. We do well to develop a sound philosophy of it.