Translation with its expanded role as a means of communication has attracted translators’ and researchers’ attention and spurred numerous debates about the optimal translation strategies for various components of language, one of which is characters’ names in imaginative literature, especially children’s literature, as they contain implications about features or fates of the characters. Nonetheless, seldom have those studies evaluated the translation strategies or provided a guideline on when or for whom to use what strategy. Also, the previous findings cannot be generalized since the effectiveness of a translation strategy may vary according to time and geographical areas. Furthermore, many strategies proposed cannot be employed to translate from English into Vietnamese. Thus, it is important to conduct a study to figure out the optimum strategies by investigating the reception of Vietnamese readers of various ages and levels of foreign language proficiency towards strategies employed to translate proper names. The research used two Vietnamese translations of Beatrix Potter’s seven children’s classics by two translators, Ly Lan and Ngo Ha Thu, as case studies. By reading and analyzing documents, administering questionnaires to 239 participants and carrying out interviews with some participants, the study found that older readers and readers whose level of foreign language proficiency is higher are generally in more favor of the foreignization and the semantic adequacy of the translated names. On the other hand, younger people and people with lower foreign language proficiency level, including most children, prefer domestication, i.e. phonologically appealing, memorable and readable names. Therefore, in order to guarantee children an exhilarating reading experience, the translator should use strategies such as phonological replacement and substitution, which can be combined with rendition and translation of connotation(s) if a name has semantic or semiotic meaning or connotation(s). Concurrently, with a view to motivating children to learn foreign languages and cultures, original names should be put in footnotes