One of the problems is that a concern for "your dynasty" is a relatively modern concept, in the form we see in game where it's effectively a surname.
The important thing was that your grandson would be King one day, whether that was via your son or your daughter. There were examples where specific arrangements would be made to keep a (personal) coat of arms alive, rather than it becoming the second coat on a joined set of arms, but those were few and far between - and generally late in the period.
One thing that was seen was the adoption of the bride's father's territorial arms by the husband, but that was generally only on assumption of her title, and more importantly he would also retain his personal arms (unless a specifc arrangement had been made).
A King would be far more willing to marry "beneath him" than to let his personal line die out, and not have any heirs at all. A Queen would be particularly so.
Overall though, it's difficult since there needs to be something to guide inheritance and game over situations, but "dynasty" isn't always a thing even at the original start date. What a noble would be referred to would change with his highest title, or his main manor if he relocated. As such over time a family that started out as "de Gunnislake" (a small village in Cornwall) might eventually be known simply as "Essex" if the line had migrated and now held Essex as their main title. Virtually no-one would remember them as being the "de Gunnislake" family, and indeed particular members might be named for the place they were born.
Henry II of England thought of himself as the heir of the de Normandy family, is considered to be the son of the d'Anjou dynasty, but could be considered the first Plantagenet (although some sources would give that to Henry III, and make Henry II and his children d'Anjou or Angevin, depending on the rendering of the name). Henry III being known as "of Winchester" after his birthplace. Other examples exist, even just counting the English throne.