Here are the name of the people and a summary of how they contributed to the notion of infinite or multiple worlds:

Anaximander (6th century BCE): The idea of infinite worlds was first suggested by him.

Leucippus (5th century BCE), Democritus (5th century BCE), Epicurus (341-270 BCE) and Lucretius (1st century BCE):  They believed in the concept of innumerable worlds.

Chrysippus (3rd century BCE): He suggested the existence of multiple universes across time which means the world eternally expired and regenerated.

William James (1895): He first used the term "multiverse". 

Boltzmann and Zermelo (1895): In a debate between them the multiverse concept first appeared in the modern scientific context.

Erwin Schrödinger (1952): He first came up with the term "superposition" by referring to his equations that seemed to describe several different histories which were "not alternatives, but all really happen simultaneously".