Right. European countries tend to use a "fixed do" system in which "do" is always "C," "re" is always "D," and so on. Whereas, in America, the "moveable do" system is used. So referring to the Dorian mode as the "re mode," Phrygian as the "mi mode," etc., could lead to even further confusion.

Already, due to the way modes are explained in some theory classes (the "all white keys" approach), some music students leap to the conclusion that pieces or songs in modes have to be played or sung with those exact pitches (only white keys, no black keys allowed), instead of whatever pitches you want, just as long as the relationship of steps and half-steps between the notes remains consistent with the particular mode. And once they get that in their heads, it takes a while to pry them loose from the notion.

No, I would just bite the bullet and memorize the scale structures and the Greek names for them, and not risk stirring up even further confusion.

Them's my sediments. . . .

Don Firth