Is the reason that Alpha sessions and Beta sessions are named those because of WHICH session did the ectobiology? Karkat, the post scratch, did ectobiology. His session was Beta. John, the pre scratch, did ectobiology. His session was Beta. Am I right on this, or has this been brought up before in canon?

Actually the Alpha and Beta sessions are named such after the version of the game played.  John played the Sburb Beta thus Beta kids.  Jane played the Sburb Alpha, thus Alpha kids.   To the best of my knowledge Karkat’s group just played Sgrub, no alpha or beta about it.