Cultural differences are always the great challenges for translators in the translation process. When dealing with cultural barrier, metaphor is a typical struggle, in which Proper names necessitate consideration because the translation might cause confused and misunderstood as well as negative feelings of the readers to the original text. A name can be popular used in a source culture (SC) or a country but too strange or the taboo in a target culture (TC). This study, by applying both qualitative and quantitative research methods, has described and compared the translations of proper names in the Shakespeare’s Romeo and Juliet and its Vietnamese translation by Dang The Binh. The findings reveal that besides similarities, when using popular proper names, English and Vietnamese cultures have many different names that require careful analysis and understanding of the translator. It is concluded that foreignization and domestication should be applied flexibly in order to introduce a friendly translation that honors both the SC and the TC.