Pili kūpuna. A term much more fitting than “endogamous” which the dictionary defines as, “the custom of marrying only within the limits of a local community, clan or tribe.”
From a Hawaiian perspective: pili ma nā kūpuna. Adhering by way of forebears. Basically what it translates to is a relation to the ancestors; that is, more distant relationship which belonged to the granparentsʻ generation or before. Based on two words, pili and kupuna.
There is an ʻolelo noʻeau (proverb) that says: he ʻohana kiko moa. “Family that hatches like chickens.” It was an expression used to mock those who mated with no regard to relationship. In ancient times, intermarriage was encouraged among the high chiefs, not for the commoners.
This emphasizes the fact that Hawaiians were not necessarily intermarrying on purpose, as it was strictly reserved for the chiefs. More so after the arrival of the missionaries in 1820 and since then even the chiefs stopped intermarrying, followed by an influx of immigrants from various parts of the world such as the U.S.A., Europe and Asia. And although we are aware of who are relatives are, and the fact that we do not necessarily intermarry our own known close relatives, we can still come up as a close cousin match. Which is why endogamy is not really an accurate term, since it was not really the custom. I cannot speak for other Polynesians, but definitely not among Hawaiians who have been isolated for at least 500 years. And we are still closely related on a genetic level to Maoris of New Zealand and other Polynesians.
Pili kupuna definitely fits as to how Polynesians relate to each other, culturally and of course genetically.