).
And sorry to be so vague. My product is actually a reusable book
cover which adjusts to any size book. It replaces your dust
jacket, and remains on the book while you read it. 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. I hope that
helps. Booklover,
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.
Jeannie
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)