What is "a label for a book identifying its owner" called?

Solution 1:

It’s a book-plate, in the OED’s definition:

A label, usually pasted inside the front cover of a book, bearing the name or crest of the owner, or other device indicating ownership, position in a library, etc.

Solution 2:

As wikipedia says -

A bookplate, also known as ex-librīs [Latin, "from the books of..."], is usually a small print or decorative label pasted into a book, often on the inside front cover, to indicate its owner. Simple typographical bookplates are termed "booklabels".

Also, In the United States, bookplates replaced book rhymes after the 19th century.

Solution 3:

It is an "Ex Libris" bookplate (or stamp), usually placed on the inside of the front, whereupon one writes one's name as owner of the book (or orders them pre-printed with one's name).

This is a popular one in the US.