This article originally appeared in the January/February 2018 issue.
While they don’t necessarily have to be, naming patterns (see Jottings #1, Freelance Traveller, November/December 2017) can be influenced by inheritance patterns and patterns of exercise of power (where the latter two can but need not be linked). This is a summary of some inheritance/power patterns that have been described as existing in the real world or in published fiction:
Cognatic Primogeniture: Descent in the senior male line only. If the line becomes extinct, go back to the most recent generation where the heir had a brother, and follow the brother’s line—through males only—to the present day. This was a relatively common pattern among European royalty. (An obvious variation on this could be female ‘cognatic’ primogeniture, which appears to be the canonical [or at least semi-canonical] mode for inheritance in the Matriarchy (and thus for the Duchy) of Mora.)
Agnatic Primogeniture: Descent may be through female lines, but preference is given to male over female, even if the female is the elder. In Absolute Agnatic Primogeniture, no preference for males is recognized; the eldest is the heir, regardless of sex. Until comparatively recently, some Commonwealth countries specified Cognatic Primogeniture; others specified Agnatic Primogeniture or Absolute Agnatic Primogeniture, and the result was that in the event of siblings, an elder sister and a younger brother, being potential heirs, or if the only direct issue of the Monarch was female, but there was a male cousin, it was possible for each to be considered the monarch of some Commonwealth countries, but not others. The Perth Agreement, negotiated in 2011 and declared to be in effect in 2015, specified that all Commonwealth countries were to pass local legislation affirming absolute agnatic primogeniture for the respective crowns, and all such legislation was to take effect simultaneously.
Discussion in several Traveller forums, and possibly attested in canonical material, suggests that traditional Vilani (including, or perhaps especially, Luriani Mmarislusant [See Minor Alien Module 1: Luriani, and “Funny Fish”, Freelance Traveller) use absolute agnatic tercerogeniture—that is, the third child inherits (per the referenced material, presumably the first becomes a shugilii, the second goes into the military).
One possibilty that leaves inheritance an open question as long as possible is ultimogeniture—the last child (subject to e.g., cognatic restrictions) is the one that inherits.
Matrilineal descent can complicate matters, especially if power vests in the male. In matrilineal cognatic primogeniture, your son isn’t your heir; rather, it’s your eldest sister’s eldest son that’s your heir—and your son may be the heir of your wife’s eldest brother. If it’s not primogeniture, it can get even more complex. This is claimed to be fairly common in parts of Micronesia and can lead to interesting family politics, because while your sister doesn’t own the family fortune (you do), she is the one raising your heir and he will be managing day-to-day running of the estate when you are too old to work. Be nice to your (eldest) sister, or she might raise your nephew to hate you and give you an unpleasant old age! (This also was the inheritance/power pattern of the Chosen in Farnham’s Freehold by Robert A. Heinlein, and in the story, Ponse, the central Chosen character, had to be on guard against various assassination plots by his nephew.)
The way the Warrant of Restoration is written, there's no method specified of determining the heir (trust me on this; I wrote the thing), and the Moot pretty much is expected to confirm except in cases of obvious incompetence. That implicitly leaves it up to the dynast to decide, and the “current” Alkhalikoi dynasty appears to use absolute agnatic primogeniture. There’s nothing to say, though, that the heir can’t be determined simply by the Emperor nominating some individual he deems appropriately deserving, or adopting such a person. (Canonically, Cleon II essentially nominated his Chancellor, Artemsus (Lentuli) as his heir, then abdicated.) The adoption route wasn’t unknown among the Romans, either; Octavianus (Caesar Augustus) was adopted by Julius and named as his heir.
In the world of Randall Garrett’s Lord Darcy, the Plantagenets still rule the Angevin Empire, and reign over the Germanies and the Italian States. Imperium for the latter was declared at some time in the past to vest in the current Angevin king-emperor of the House of Plantagenet, and while cognatic primogeniture was expected, technically, the Angevin parliament could choose one of the other Plantagenet princes to become King-Emperor instead.
While it was in reality no doubt a bit messier than this description makes it sound, the old Soviet system essentially named a premier for life, and on his death—which might not have been natural—the Supreme Soviet elected his replacement. Arguably, modern republics—and most constitutional monarchies—use a more benign form of this. (Yes, election is a legitimate method of determining inheritance. For non-power inheritance, there’s no reason that a family couldn’t do something similar, and a will naming heir(s) is, essentially, a statement of election of heir(s) by an electorate of one.)