The research is focused on the problem of personality reaching its self-identity through identification and de-identification with the Self through the significant Other during a reflexive dialog. Personological approach was used to solve this problem, based on consistent creation and mutual refraction of conceptual, cultural-phenomenological and reflexive-dialogical models of identification and de-identification of I with Self in relation to the Other. The research is interdisciplinary in nature, based on domestic and foreign sources relevant to the study of self-identity. The article presents the results of an empirical study conducted with the method of reflexive interviews and devoted to the research on internal dialogue between the Self and the Other; the subject of the study was the respondents' quality of "openness to experience." The novelty of the study consists, firstly, in raising the issue of self-identity in terms of paradoxically inseparable unity of identification and de-identification with the Self as opposite to self-actions. Secondly, the research offers psychological consideration of the importance of the Other in mediating the acts of identification and de-identification of I with Self during a reflexive dialog between I and the Other. Thirdly, the existing understanding of the genesis of the dialogical Self is enriched by the idea of the structure of dimensions of the internal dialog I - Other, considered as the dynamics of identification and de-identification of I with the Self. Fourthly, the processes of identification and de-identification with the Self and reaching self-identity are analyzed from the point of view of search and discovery of the unknown Self. Fifthly, empirical research resulted in defining of the forms of self-identity in the aspect of openness to experience, which depend on the level and dynamics of identification and de-identification of I with the Self though the Other. There are developing, maturing, controversial, rigid and regressing self-identity among those forms.