What is the place called where cheese is aged?
I don't think there's a specific name for it.
I found a book that simply refers to it as an &quot;aging space/room&quot;.

The Aging Room: The &quot;Big Three&quot; Design Issues
When designing an aging space, there are three main factors to consider: temperature, humidity, and air (both air exchange and movement). Each of these factors will be influenced by the volume and type of cheese being aged; your area's native influences (weather and soil/earth stability and properties; also if your building is underground); and the building structure and size.
The Small-Scale Cheese Business: The Complete Guide to Running a Successful Farmstead Creamery p. 126

Around the web, I've seen it referred to as a &quot;cheese cave&quot;, which refers to the historical habit of using caves for aging cheese.

How to Make a Cheese “Cave” - This is a guide on aging cheese in a refrigerator.
Crown Finish Caves - A cheese aging facility in Brooklyn, NY.
Wegman's Food Market opened a &quot;cheese cave&quot; in 2014.

For a similar reason, I've seen a smaller number of references to &quot;cheese cellar&quot;.