What is a proper noun for hospital?

There isn't a single proper noun for "hospital" in the same way that there is for "city" (e.g., New York City).

"Hospital" is a common noun, which means it refers to a general category of things. To make it a proper noun, you would need to specify a particular hospital:

* Examples of proper nouns for hospitals:

* Mayo Clinic

* Memorial Sloan Kettering Cancer Center

* St. Jude Children's Research Hospital

* The Cleveland Clinic

* University of California, San Francisco Medical Center

Let me know if you have another word you'd like to make into a proper noun!