As I read your first sentence of this thread, "adjustable totebag for books" - I actually pictured an adjustable bag that carries books. So the first name that popped out of my head was actually, Book Totes.
I didn`t read anyone else`s comments at all. Then as I read further down the thread, you said it is actually a "reusable book cover which adjusts to any size book and that there are adjustable handles so you can carry it like a tote or over your shoulder. It also has pockets large enough for basic items like keys, cash, and phone. So it turns your book into a purse. My product covers, carries, and protects your book." - which I think the name Book Totes still fits.
And then I finally read Craig`s comment and he was thinking along the same lines I did, naming it "Book Tote"! Funny how we thought of the same thing!
So, my clear suggestion would be "Book Totes".
Hope that helps.
OK, here`s a few REALLY off the wall, but they may cause someone to make a leap to something else.
The Burse... The purse for your book!
The Book-Along... Take your book along! (Naa)
The ToBo... The Tote for your Book! ( Remember, Google was not a word several years ago)