Is there a name for this style of historical novel?

The kind with a storyline of centuries or even millennia, telling the story of a given city or region or country over many generations, perhaps using related characters with a given genealogy. The most famous author of this kind of novel – and, for all I know to the contrary (I’d be happy to be proven wrong), its inventor – was the late James Michener. A living one is Edward Rutherfurd.

I think you gave away the term already. Generational.

“Epic” – perhaps?

Saga ?

Family saga” is in the same ballpark, but I think the OP is looking for a work whose unity is primarily based on geography rather than genealogy.

Ken Follett transitioned from spy thrillers to these types of novels.

Right. Michener’s The Source is the story of Jews in all countries, but what ties it together is the archaeological site at Makor in Galilee.

Similarly, Michener’s Chesapeake is the story, not even of the bay as a whole, but of a small chunk of land on the Eastern Shore, and the people who live there at different times.

IMHO, the genre should be named after Michener.

“Epic” already has a literary genre definition focusing on a hero’s journey (a bit of a there and back again approach).

I loved his Pillar of Earth books. His thrillers are rather meh.