"We come together today to unite in marriage..." or some variation of these words are the standard prologue to the wedding ceremony. To unite - to make one or to form a union - is the whole purpose of marriage. It is a coming together of individuals to form a single entity, or at least, such is the traditional purpose.
When a couple joins together, they are making a commitment to work together as one, to live as one, and to place the union ahead of either individual. The sharing of a common name is symbolic of their unity. Retaining separate names is a declaration of individuality, separate autonomy, and a denial of this unity.
Consider other unions, such as a sports team. Here, a group of players gather together with a common purpose in mind (winning the game) and they contribute their skills to the success of the team. Sacrifices are made along the way, as not every player can take on their favorite roles, personal lives are put on hold when extra practices are needed, and team uniforms rarely flatter everyone's appearance. And every team has a name. That name identifies its members more than anything else. Few people know all the player's names of every team, but name the team itself (the Red Wings, the Yankees, the Dolphins...) and most everyone knows exactly who you are talking about. Fans think of individual players as "one of the Bears" or "a Wolverine". They recognize that the individual has become a part of a greater whole. When a player chooses to act more as an individual than as a teammate, they are viewed as harming the team, and behaving selfishly. Obviously, the same observation applies to marriage.
If one partner wishes to put their own interests before those of the union, then the marriage is weakened. If a couple is to be united as one, they need a name to rally behind, just as any team does. Quite frankly, it really doesn't matter if it is the last name of the husband that is adopted. This is a cultural tradition in patriarchal societies only. In other societies, it is the wife's name that is adopted for the family. Either way, the name reflects the idea of "two become one", a single functional unit that is ready to face the challenges of life together. A couple could even decide that they dislike both last names, and legally change over to a completely different name. If the decision were a joint one, a team effort, then it could only be a move that strengthened the union.
People may wonder how something so innocuous as retaining separate names could harm a marriage. "What's in a name, anyway?" they might ask. We have already established that a common name is a symbol of unity. The converse is also true. Separate names are a symbol of disunity. It does not mean that the couple do not love and care for one another. It does mean, however, that there is unwillingness to compromise. No two individuals are going to agree all the time, and there will be a need to approach such issues. If a couple cannot agree to act as one in something as simple as a name, imagine how difficult they will find it to deal with job changes, relocations, debt collectors, and how to raise the children - all items with great potential for stress and disagreement. If the pair chooses to act unilaterally, trusting only in their own judgments and discounting their partner's, conflicts and chaos must emerge. Such a marriage is doomed to hardship.
It would be wrong to say that having separate names causes such marital problems as we have mentioned. The rejection of a shared is only a symptom of a lack of unity. The other issues that surface later are also symptoms of that lack of unity. In the end, when a marriage fails, it is also because of that lack of unity. So if a couple is unwilling to act as one in choosing a name, it might not be a bad idea for the couple to rethink whether they are actually ready for marriage.