Continuing with Xap's explanation, it's a bit different than in the US. ONLY the wife can add the "de" clause (at least in Spain, where nobody does it anymore). Informally, my wife can be referenced as "Sra. de MyLastName" (Mrs. of MyLastName, denoting she's my "property") even if she didn't change it officially. Only very old people use that nowadays, and, at most, they call her Mrs. MyLastName (also seldomly used).
We get two last names (one from the father, and one from the mother. Usually in that order). In your Rogers-Martin example, I guess both are called Rogers-Martin and their kids will be called Rogers-Martin.
If Mr. Fernández González marries Ms. García Sánchez, she can change her surnames to García de Fernández Sánchez. The underlined part becoming her first surname. But their kids will be Fernández García, not Fernández García de Fernández.
Yes, we are weird.
Here, in the small Iberian Rectangle, we do it differently.
3 options:
1- The married couple DON'T change their names. The most common nowadays, mostly because it is a PITA to change it back after a divorce.
2- The married couple BOTH change their names. Rare, but possible, this takes the form of appending the last surname. We get 2 surnames, the first one called "Matronímico" is from Mother's last surname, the 2nd called "Patronímico" is the last surname of the Father. In effect, it is derived from the surnames of our Grandfathers. When adding a last name both change the surname to one of theirs. They have 4 to choose from.
3- The married couple only ONE change their names. This was the rule for centuries, the wife would add the husbands "Patronímico". There are cases, as in my family, where the surname is composed of 2 surnames connected by a "de", in this case, it is the choice of the married couple, if they append the full surname or only one of them. This tends to make women's names incredibly long with 3 or 4 surnames besides the traditional 2 names.
Wars and Feuds were fought over these rules. Lineages and "Families" all exerted pressure over the married people to force the adoption of what rule was more favorable to their plans.
It may sound weird that people marry already making plans for what could happen in a divorce, but if you think about it, it makes complete sense. The romantic version "married forever", is no longer a credible option to anyone with a modicum of intelligence. It may happen, it may not... let's be smart and make provisions to make our life easier.
I know of at least 10 couples, that married, divorced, still live together, raising their children. What type of arrangement they have in the bedroom(s), is what works for them. Some are open, some are half-open (not always the husband), some are closed. And some are whatever and everything goes. In these cases, the naming conventions stopped making sense a long time ago.
Peace
