I'm not aware that Tolkien ever gave all of the names of the wizards, but I could have overlooked something.
Of course there are Gandalf, Saruman, and Radagast, but the rest, as far as I can recall, are merely mentioned as having existed, and never come into any of the stories.
Oh, but how about the other name(s) of Saruman? I know at only one, but there may be more.
And as to other names for Gandalf, I don't think anyone has mentioned the Steward's name for Gandalf: "the grey fool".