Mordenkainen's Tome of Foes goes into heavy detail on the nature of the dwarven clan, describing the clan as "[...] the basic unit of dwarven society, an extended family that dwells together".
On the topic of marriage, however, it says: "marriage is a sacred rite among the dwarves, taken very seriously because it requires two children to move away from their homes to start a new family in the clan", and that Berronar Truesilver's priests arrange marriages "to ensure that each generation of a clan is stronger and more talented than the last" (emphasis mine), possibly implying these are dwarves from separate households/branches within the same clan branching off to start a new family within the clan. It also says that "a clan is led by a king or a queen who sits at the head of a noble family", when those are titles I generally associate with an entire city/kingdom's leader.
The book does not particularly go into the nature of dwarven cities (focusing on the nature of strongholds instead), or go much into the nature of interactions between clans. I take from the above that it is typical that a dwarven city belongs to a single clan; Sword Coast Adventurer's Guide implies at least that this is certainly the case sometimes, mentioning Thornhold belongs exclusively to Clan Stoneshaft, and mentioning that Mithral Hall was the ancestral home of a particular clan.
Does this mean that dwarven clans are of extremely extended families, given the implication that they mostly interact/marry off within themselves? (And if so, do they tend to have different last names in order to distinguish the branches from one another, or do they all share the clan name, as the PHB's Dwarf Names section implies?) Or are some of my assumptions incorrect, and interacting with/marrying into other clans is more commonplace than Mordenkainen's Tome of Foes implied to me?
To clarify, the impression I have from reading these two books is that clans have the overall population of up to a small city and therefore have enough diversity/separation to support intraclan marriage as the norm, but there's not quite enough in the books to leave me certain that that interpretation is correct.
(Answers using lore from other editions are acceptable, so long as there's no reason to believe it is no longer valid.)