Yes, in the hilltop scene he DOES call her by her maiden name. And in the scene after her death, Dumbledore keeps pointedly referring to Lily EVANS's eyes, Severus's love for Lily EVANS... Lily's son.

But Severus actually agrees to protect "Potter's son"--provided that that entity is never told why.

And you're totally right, by sixth year it was "Lily Potter's son" whom Dumbledore had raised like a pig for slaughter.