What is the possessive noun in this sentence Angela Badger books were about girls with lots of problems?

There is no possessive noun in the sentence.

The proper noun Angela Badger is functioning as an attributive noun to describe the noun books. An attributive noun (also called a noun adjunct) is a noun that functions as an adjective to describe another noun.

The sentence with a possessive noun is:

Angela Badger's books were about girls with lots of problems.

An apostrophe s ('s) or just an apostrophe (') added to the end of a Word forms a possessive case noun.