Tragicomic is correct that both "me" and "story" are objects of the verb "told" in the sentence "he told me a story," but they're not the same kind of object: "story" is the direct object, "me" the indirect object. You can find each by asking a series of questions using already known part of the sentence.
Beginning with the subject and predicate, add "what": He told what? The answer, a story, is the direct object.
Next, ask a question using the subject, predicate and direct object, and add "to whom" or "to what": He told a story to whom? The answer to this question, "me", is the indirect object.
Applying the first question to the original sentence yields this: Behavior risk what? The answer, "damaging a company’s brand and reputation" is, as Tragicomic said, the direct object. Direct objects are always nouns. In this case, the phrase begins with the "ing" form of a verb which, when used as a noun, is a gerund. Since it's grouped with a bunch of other words, the object is a gerund phrase. Within that phrase, we can play some of the same fun games we played with the sentence as a whole, asking "damaging what?" to get the direct object "brand, reputation" of the verb damage.
The fact that all this takes so long is one reason why, when I'm teaching English, I keep the grammar to a minimum.