At his last US seminar, Saito Shihan told the group that when O Sensei was teaching at Iwama, they'd slowly learn ikkyo, then nikyo, then, as they thought they'd learn sankyo a new student would arrive...he'd start them over, they'd learn ikkyo, then nikyo, then as they thought they'd learn sankyo, a new student would arrive...he'd start them over...and so they'd then beat up the new student.
I liked the variety when I started, but this might
help. First, don't worry too much about learning entire techniques, because as you've noticed, they change in subtle and not too subtle ways. Work on learning to watch. Watch your sensei's feet, where they move to as he does technique, repeat the steps to yourself as you watch. If he's still demonstrating and you have got the foot work, try to pick up some of the hand movements. By then he will be done, but you will have 2-4 more chances to see it, since the senior (grab a senior) partner will go first. Pay attention to how your body feels as he moves it.
As for learning the names, if your sensei doesn't either say the name or write it down when it is shown, but allows you to ask questions, ask then what it was. If not, then after class ask a senior. After or before class, ask a senior to work with you on one technique. Take notes.
I wouldn't rely on books or tapes, etc, unless they are put out by your sensei...styles and sensei's differ, the only 'right' way is the one you are shown, and the same instructor may do it differently depending on the uke, etc.
It seems like an awful lot to learn at first, but you'll be surprised in how short a time you find yourself yawning to yourself and thinking 'oh, not ikkyo AGAIN'.