Either choice can have an impact on the relationship and on the status of each partner in the relationship. If she takes her husband's name, there is the bother and expense of changing names, but she avoids making waves and she affirms that they are now a family melded into one name. She can count on the support of those who are comforted by her act. If she chooses to keep her own name, she need do nothing, but she might get remarks from those who are discomforted by her not taking her 'place'. Mostly, if she does not make an issue of it, it is not an issue.
Some women report that every time they write or speak their name, they feel empowered.
But those are just the practical or social consequences. Anyway, my name is my father's name. Many women still decide it is easier to change credit cards, driver's license, social insurance card, business cards and become untraceable to their childhood friends, than it is to assert their own separate identity. The custom of taking the husband's name is not universal. In some countries, women have always kept their name.