Your premise is ridiculous.
Woman keep their maiden names for a variety of reason, like a professional degree in the maiden name.
In many cultures the husband takes the wife’s name.
Some cultures women would think it was silly to take the husband’s name.
In some areas of the word a new family name is given.
In my case I took my husband’s name because it was way more interesting than my ordinary maiden name.
My mother kept her maiden name because it was way more interesting that her married name would be.
I do find it interesting that you appear to attach “healthy” marriage to cultural symbols.
If my premise is ridiculous, then so is everything that underpins Western civilization. Degrading or discounting the symbols of marriage is the first step to degrading the institution itself.
You can argue that other cultures do things in other ways, but that's not how it's done in this culture. In fact, our way predominates around the planet.
Cultural norms, like those of western-style marriage, come about because over long, long periods of time, people see that some ways of doing things lead to better survival for the group, and other ways of doing things lead to lowered survival potential for all concerned.
In our oh-so modern world, we're throwing away hard won centuries of valuable knowledge and cultural norms with wholesale abandon. The high divorce rate of today ought to give one a clue that maybe we're throwing out the baby with the bath water when it comes to familial unions.