The adoption of one’s husband’s last name is clearly not limited to Nigeria, and its implications are even more far-reaching than you mention. For one thing, as same-sex marriage becomes more common, the notion of attaching name to gender becomes less meaningful. Also, I have personally experienced an unintended consequence of adopting last names: I am in a committed relationship with a woman who chose not to take her former husband’s last name. Her children have their father’s last name. When we all travel together, especially abroad, having children whose last name doesn’t match either of our last names can be problematic.
The Spanish have a slightly better approach, where people adopt a double last name, although the father’s is always first and thus is more enduring. A new way that gives equal recognition to both parents would be a step forward in promoting equality.