Translating names in non-literary works, i.e. in scientific, technical or journalistic texts, does not pose too many problems. With literary translations, however, the situation is different. Here each case is individual, and when making decisions, the translator must consider all possible implications of his choice. The problem has been given some attention by the theoreticians, but they do not give clear guidance in everything that the translator may come across in his practice. To a large extent, he has to use the trial-and-error method. In such a situation, it might be useful to look at some of the decisions made by other translators, in order to profit from their successes and to avoid repeating their mistakes. The examples in the paper have been taken from Polish translations of English and American literature as an illustration of the problem.