The idea of a woman changing her name on marriage is clearly a non-Jewish custom. Traditionally a woman would be known as “Pilonis bar [father’s name]” for her entire life. The goyim started to force Yidden to adopt family names a few centuries ago (the better to tax and conscript us), which explains why Jews have been very unattached to their surnames and frequently change them (by way of contrast, many western European goyim have surnames that have been in use for thousands of years, and are critical in researching ancestry). Rabbanim have allowed women to adopt the husband’s surname even though it is a goyish minhag (as are inherited surnames).
While there are no “Jewish” arguments on change of surname, there are practical reasons for the wife to adopt a husband’s name, especially if they expect to have children and if they are going to be on the same health insurance.