"特殊神宠论" can be translated as "The Theory of Special Divine Pets" or "The Concept of Special Divine Companions" in English, depending on the context and intended nuance.
"The Theory of Special Divine Pets" emphasizes the idea of a theoretical framework or doctrine concerning special, divine-like pets.
"The Concept of Special Divine Companions" focuses more on the notion or idea of having special, divine-like companions, which might be a more poetic or philosophical interpretation.
Choose the one that best fits the context in which you intend to use it.