The article is devoted to the problem of identification of a language personality's traits under conditions of cross-cultural communication. It is shown that effective cross-cultural communication is revised under globalization and increasingly intensive social interactions. The results of the authors' research prove that it is possible to develop a new perspective on the heuristic possibilities of the concept of language personality to ensure the effectiveness of cross-cultural communications. This applies above all to the understanding of culture, cultural codes, verbal, non-verbal communication and preverbal, development of value measurement and understanding, and behavior adoption patterns. We propose to identify a language personality as a nationally specific communicant type that has a culturally caused worldview and value system and is capable of cross-cultural transformation. We identified transitions from a "mono" language personality to a "multi" language personality. We offer communicative training as a way of resolving cultural gaps in communication. We insist that only a new type of a language personality can effectively integrate and communicate while taking into account cultural peculiarities. Language personality currently acquires multicultural traits resulting from two main types of mobility: virtual and physical. Empirical research shows that two types of mobility are widespread, with typical high demands for the study of an international communication language (English) and local culture (Hebrew).