The name of Ram Prasad Bismil is associated with the Kakori Conspiracy Case. The Kakori Conspiracy Case was a major event in the Indian independence movement against British rule. Ram Prasad Bismil, along with other revolutionaries, planned and executed the Kakori train robbery on August 9, 1925. The aim of the robbery was to obtain funds for the revolutionary activities against the British government.

Option 1, Kanpur Conspiracy Case, is incorrect. The Kanpur Conspiracy Case refers to a separate incident where Bismil was also involved, but it is not directly associated with his name.

Option 2, Alipore Conspiracy Case, is also incorrect. The Alipore Conspiracy Case was a different trial that involved the assassination of a British judge and was conducted in Alipore, Kolkata.

Option 4, Meerut Conspiracy Case, is incorrect. The Meerut Conspiracy Case was another significant trial that involved several communist leaders and revolutionaries, but it does not involve Ram Prasad Bismil.

Overall, the correct answer is option 3, Kakori Conspiracy Case, as it is specifically associated with the name of Ram Prasad Bismil.