Those would be examples of matrilineal marriages, right?
Let's call it for what it is; the concept of dynasty, as understood by the game, modelled on Western Feudal ideas, doesn't translate well in Byzantium, where the name carries prestige, not blood, and the name will change if circumstances are right.
As I said before, Byzantium needs a ton of tweating if Paradox wants the Byzantine experience to be not only genuine, but also interesting.
I mean, matrilineal marriages are a game construct. You can’t really describe either of the marriages I pointed out as matrilineal marriages, because the concept of it didn’t exist. What usually happened in Byzantine society is that the child would take the name of his most prestigious line. It was, however, ultimately dependent on how the child chose to style himself in later life.
Taking the aforementioned example, a general named Theodore Komnenos Laskaris married Anna Angelina, a daughter of Emperor Alexios III Angelos. Since Alexios had no sons, Theodore eventually became his expected successor (heir is an alien concept in Byzantium). He eventually became known to posterity as Theodore I Laskaris of Nicaea. The children of Theodore and Anna were styled as “Komnenos Laskaris”, with mentions to their Angelid ancestry being rare (most likely because the family was disgraced and because the Angelos family was competing with the Laskaris family for hegemony over the Byzantine successor states after the Fourth Crusade).
A generation later, Theodore I’s eldest daughter, who went by the name of Eirene Komnene Laskarina, eventually married the general John Doukas Vatatzes. Despite being a Vatatzes by patrilineal descent, John almost never went by that name, usually signing as just John Doukas instead. This is because Doukas had been an imperial dynasty, so John wanted to emphasize his matrilineal descent from the Doukas family. He eventually succeeded Theodore I and reigned as John III Doukas of Nicaea. He remained emperor even after his Laskarid wife retreated to a monastery and died prematurely.
Fast forward another generation and you have the child of John III Doukas Vatatzes and Eirene Komnene Laskarina, who would become Emperor Theodore II. In adult life, Theodore II was styled as “Theodore Doukas Laskaris” or simply “Theodore II Laskaris” (in sources “the second Theodore of the Laskarids”). He ditched his mother’s Komnenos line, but adopted the Laskaris name as his principal dynastic name, while also keeping Doukas as his middle family name. Theodore I, John III and Theodore II are all considered to have been part of the Laskarid dynasty.
Family tree for easier comprehension (dominant family name boldened):
- Emperor Alexios III
Angelos
-- Anna
Angelina, m. Emperor Theodore I Komnenos
Laskaris
--- Eirene Komnene
Laskarina, m. Emperor John III
Doukas Vatatzes
---- Emperor Theodore II Doukas
Laskaris
This type of arrangement also happened as soon as the 11th century and in non-imperial contexts. For example, Caesar Nikephoros Melissenos, a powerful general and governor of Thessalonica, married a sister of Alexios I Komnenos. All of his children preferred the style of Komnenos over Melissenos, because Komnenos was the more prestigious name as it was the ruling dynasty.
I understand that, but CK is built on the concept of playing dynasties. So if you make your son-in-law your heir and he isn't of your dynasty it's game over. So adopting him into your dynasty wuold be how it could work within the limitations of the game.
This game is not 100% historical for any part country on the map, so even the Byzantine Empire must contend with abstracting some things for the sake of gameplay.
They could make it so that if you adopt a son-in-law he changes to your dynasty, but automatically creates a new cadet branch with only him as a member, with the coat-ot-arms and name being a combination of your and his original dynasty.
Of course, I’m just musing possibilities to accurately simulate the context were are dealing with. In the HIP mod for CK2 you had a game rule for allowing a non-dynastic successor. The same could be done for CK3, as long as said successor was married matrilineally to a woman of your dynasty and his children were of your dynasty. You would still be playing as your dynasty. His birth family doesn’t matter, only his dynastic affiliation. In the example above, John III Doukas Vatatzes should remain a Doukas Vatatzes, but for gameplay purposes he should be considered a non-dynastic heir (and head) of the House of Laskaris because he effectively led the family during the time period and his son continued the Laskaris name and line as his principal dynastic affiliation.