The tradition of a wife taking her husband’s last name at marriage is not found in the Bible. In Bible times, most people did not even have last names. Women were often identified by where they lived (e.g., Mary Magdalene, Luke 8:2), by their children (e.g., Mary the mother of James and Joseph, Matthew 27:56), or by their husband (e.g., Mary the wife of Clopas, John 19:25).
In Western culture, it has been a common tradition for a wife to change her last name to that of her husband. The vast majority of married women in the West still follow that tradition. There is nothing explicitly biblical about doing this, since the Bible issues no command to do so. Thus, there is nothing explicitly unbiblical about a wife keeping her maiden name or opting for a hyphenated hybrid.
Some women who legally change their last names after marriage are simply following cultural conventions. Many others, however, are consciously choosing to illustrate a couple of biblical principles, namely, the headship of the man and the fact that marriage is the union of two people into “one flesh.” Jesus taught that, when a man and a woman are married, “they are no longer two, but one flesh” (Mark 10:8). A common ritual during wedding ceremonies is the lighting of the unity candle, which illustrates Genesis 2:24, “A man leaves his father and mother and is united to his wife, and they become one flesh.” The husband, as the head of the home and the nurturer of his wife (Ephesians 5:23), shares his name with her, rather than vice versa.
Other cultures may have different traditions regarding a woman changing or keeping her last name after marriage. Again, since the Bible does not specifically address the issue, the matter should be decided based on prayer, cultural considerations, and the wishes of the husband and the wife.