"中国的殷代" can be translated into English as "the Yin Dynasty of China" or more commonly and conventionally referred to as "the Shang Dynasty in ancient China" (since the Yin Dynasty is another name for the Shang Dynasty in historical contexts, and "Shang Dynasty" is the more widely recognized term in English).
Here, "Shang Dynasty" is the standard and most commonly used English translation for 中国殷代, as it is the accepted historical name for that period in Chinese history. If emphasizing the alternative name "Yin," one could say "the Yin (or Shang) Dynasty," but "Shang Dynasty" alone is sufficient and preferred in most contexts.