We all have some identities that we do not identify ourselves with; this is just normal, for a person can have a strong and stable sense of who he is only if there are not too many things that he thinks he is, that he thinks define who he is. It would not be a problem if a person alienates himself from some, or even many, of his identities, but it would be a serious problem if he alienates himself from all of his identities. When a person has no identities that he identifies himself with, he is alienating himself from his whole biographical life. In that case, he is indeed alienating himself from himself, for some of his identities must define who he is in order for him to be the person who is living the biographical life that he is living, to be the I who would own the first-person version of his biography, i.e., his autobiography. As Camus so vividly and penetratingly portrays it in L’Étranger,* the life of a person who alienates himself not only from the world around him, but also from himself, is a meaningless life to the person himself.
* “Étranger” in French means either "foreigner", "outsider", or "stranger". Some English translations use the title The Stranger, some the title The Outsider. The protagonist Meursault is a stranger, a foreigner, or an outsider not only to people around him, but also to himself.