What does "Fangcang [hospital]" mean?
Edit: 

After reading fefe's comment, I did more search and found this 方舱医院是什么


  方舱医院是以医疗方舱为载体，医疗与医技保障功能综合集成的可快速部署的成套野外移动医疗平台




So  "方舱" is obviously referring to those rectangular mobile units. 

方舱医院 should be translated as "mobile cabins hospital"

As for the relationship between 方 and 方舟, may just be a coincidence 

It is easy for people who never heard of 方舱 to link  方 with 方舟, due to the current crisis. If 方舱医院 didn't exist before this pandemic, my previous theory would be a fitting one

Previous theory: 

"Noah's Ark" in Chinese is 「諾亞方舟」 or 「方舟」 (literally mean 'square ship')
「方艙」(Fangcang)  is made up of 「方舟」and 「艙」(cabin)
"Fangcang hospital" literally mean "Cabins of Noah's Ark hospital"
We all know what the term 'Noah's Ark' implies