Saturn and Rhea, while Herodotus identified her with Demeter. (Others again identified her with lo.) Plutarch says that she married her brother Osiris and that she reigned jointly with him in Egypt.
Whoever she was as far as the Greeks were concerned, her name is obviously not Greek. It is in fact a version of an ancient Egyptian hieroglyph meaning 'throne'. As this was feminine, she symbolised the mother of the king since the throne 'created' the king.
The modern name Isadora or Isidora is usually held to mean 'gift of Isis', with the latter half of the name being Greek doron, 'gift', 'present'. How the name was first popularised is not clear - probably through some literary character so called or as the feminine of a (real) man's name Isidorus, which was quite common in Greece. It is possible, however, that the first part of the name does not after all derive from Isis.