I think there isn’t a specific word for an “armor holder” because we don’t have heavy suits of armor that need to be suspended that way. We do have other heavy things that we suspend to work on, like engines, or use a device to help move around because they’re heavy, like large animals.
I think the term “lift” (A machine or device designed to pick up, raise, or carry something.) or even “armor lift” would apply. For example, this is a “truck lift”:
Lifts make heavy things easier to work on by suspending them at convenient heights. I’m not sure it completely captures the device in fallout, because I don’t think we typically store things on lifts.