Recently, psychological phenomena have been expanded to new domains, crisscrossing boundaries of organizational levels, with the emergence of areas such as social personality and ecosystem learning. In this contribution, we analyze the ascription of an individual-based concept (personality) to the social level. Although justified boundary crossings can boost new approaches and applications, the indiscriminate misuse of concepts refrains the growth of scientific areas. The concept of social personality is based mainly on the detection of repeated group differences across a population, in a direct transposition of personality concepts from the individual to the social level. We show that this direct transposition is problematic for avowing the nonsensical ascription of personality even to simple electronic devices. To go beyond a metaphoric use of social personality, we apply the organizational approach to a review of social insect communication networks. Our conceptual analysis shows that socially self-organized systems, such as isolated ant trails and bee’s recruitment groups, are too simple to have social personality. The situation is more nuanced when measuring the collective choice between nest sites or foraging patches: some species show positive and negative feedbacks between two or more self-organized social structures so that these co-dependent structures are inter-related by second-order, social information systems, complying with a formal requirement for having social personality: the social closure of constraints. Other requirements include the decoupling between individual and social dynamics, and the self-regulation of collective decision processes. Social personality results to be sometimes a metaphorical transposition of a psychological concept to a social phenomenon. The application of this organizational approach to cases of learning ecosystems, or evolutionary learning, could help to ground theoretically the ascription of psychological properties to levels of analysis beyond the individual, up to meta-populations or ecological communities.