"A name of Zeus as worshipped at Didyma in Miletus jointly with Apollo": LSJ s.v. (web address 1)
This epithet appears to have been at first attributed to Apollo, because of the double (di/dumos literally means "twin") light this god provided to mankind: the Sun and the Moon. (Cf. the myth according to which Sun and Moon are identified with Apollo and his sister, Artemis). The center of the worship of Apollo Didymaios was a place also called Didyma, which belonged to the Milesians and was renowned for its oracle; Suetonius, Caligula 21 mentions the completion of the temple among the plans of this emperor (web address 2).
For the joint worship of Apollo and Zeus at Didyma see Stephanus of Byzantium, Ethnica s.v. Didyma and Didyme (229.20-230.4).