What type of intangible asset can include rights associated with names and logos?

Franchises are indeed a type of intangible asset that includes rights associated with names and logos. When a franchise is granted, it allows the franchisee to operate using the franchisor's brand name, trademarks, and business model, which typically includes specific logos and branding elements. This grants the franchisee the right to exclusively use those identifiers in a specific market area, creating a recognizable business presence.

Goodwill refers to the value derived from a company's reputation, customer relationships, and other intangible elements, but it does not specifically relate to the rights associated with names and logos as franchises do. Purchased patents involve specific legal rights to inventions or processes, while trade secrets protect confidential business information but do not encompass rights to names and logos in the way franchises do. Thus, franchises are the most accurate answer to the question about intangible assets associated with names and logos.