Here is the example:
We condemn such behavior that can risk damaging a company’s brand and reputation.
I think, the 'a company's brand reputation' is the object of 'damaging'. And the whole phrase is the object of 'risk'. is it right?
Your analysis of the sentence is correct. The -ing form is a present participle, which can take a direct object, in this case "a company's brand and reputation". The participle + object acts as the complement of the verb "risk".