Headband
Also called Headbands and tailbands, endband
A small roll of fabric glued at the head and tail of a hardback’s spine, between the text block and the case. Once sewn in to strengthen the binding, it is now a finishing touch.
In practice
It costs next to nothing and shows every time the book is opened, so it is worth choosing the colour instead of taking the default. Match it to the cloth, the endpapers or the ribbon. The choice is made from the printer’s or binder’s swatch card, in other words from what they stock.