The Eva cockpit with multiple screens inside that basically shows a 1:1 view of everything on the outside.

The game Titanfall has a similar type of cockpit: https://titanfall.wikia.com/wiki/File:Titan_View.png

What are they called? Is there a name for this?

Entry plug, cockpit, and very rarely, or informally, "throne of the soul". It's only mentioned once in episode 14 of the TV series, but I believe figures/models of the characters with the cockpit have used the name, and more recently, the VR ZONE SHINJUKU game "Evangelion VR The Throne of Souls : Berserk" has used it to specifically refer to the cockpit

Names from the 1.0 CRC:

The whole thing is the "Entry Plug", the part where the pilot sit and control the Eva unit is called "Interior Array Inside Entry Plug", the 360° screen is called "Pilot's Display Inside Entry Plug".