Jack Campin's points are the *money* points. I would put special emphasis on the idea that each *mode* is a scale that is part of a larger system music system or musical tradition that is defined by a lot of other elements, which are often more important   than the scales themselves.

And what it's worth, even though the names of the modes mentioned above are Greek, those are not the names used for modes/scales in Greek traditional music.

As to renaming, Western classical music theory evolved from church mode theory, so actually, they have been renamed--Ionian is the "Major Scale", Aeolian is the "Natural Minor", and the Mixolydian is the "Dominant Scale"--they have functions that go beyond
the possibilities of the older music forms.

The others can be given other names, too. Dorian can be called "Supertonic scale", Phrygian can be called "Mediant scale", Lydian can be called "Subdominant scale", Locrian can be called "Subtonic scale"--