The singular of people is person. For example, if there are three people in a room, you would refer to one of them as a person. There other English nouns of this type, e.g. cattle vs cow/bull. Is there a name for this class of nouns in which the singular and plural forms are not related?
From the Wikipedia article on suppletion:
In linguistics and etymology, suppletion is traditionally understood as the use of one word as the inflected form of another word when the two words are not cognate. For those learning a language, suppletive forms will be seen as "irregular" or even "highly irregular".
It gives both cow/cattle and person/people as examples, though person/people is “incomplete suppletion”. Suppletion covers more than just nouns though, including verbs like be/am/is/was/were, so the term you are specifically looking for is suppletive plurals (example).
The singular of people is person.
People and person are different words.
The plural of people is peoples; the plural of person is persons.
However a group of persons has a collective noun "people" that is in the singular but with plural agreement.
Thus we have:
1994 Dog World Aug. 112/3 Respect for a companion, whether the companion is a dog, a cat, a horse or a person is very important.
1963 E. H. Schafer Golden Peaches of Samarkand ii. 52 The great Hsüan Tsung himself, like many other noble persons, was a trained performer on the wether drum.
1991 Bellcore News 15 May 3/2 I think we should trust our people more; I think we have too many people in management.
2000 Guardian 2 Dec. (Travel section) 11/1 The Domesday entry..shows that the people of Laxton were cultivating about 720 acres of arable land.
1792 R. Bage Man as he Is III. lxv. 118 It has been usual to suppose the English a people who bore misfortune with passion or with gloom.
1999 N.Y. Rev. Bks. 22 Apr. 54/3 The Ruthenians are a part of the family of east Slavic peoples.