Is there a system where multiple people can encrypt a message and then decrypt it in any order? For example, A encrypts a message.

B encrypts that.

C encrypts that.

Then B decrypts, followed by A then C.

Are there systems that allow this? Does such a property have a name?
Yes, systems that allow this have a name: commutative encryption.

In practice, there are two varieties:


If A, B, C just xor in a keystream, it all commutes.  Of course, anyone seeing the intermediate results can deduce quite a lot; this may make this unacceptable for some uses.
Pohlig-Hellman (not related to the Pohlig-Hellman algorithm); we pick a global prime $p$, and everyone selects a secret value relatively prime to $p-1$; A picks $a$, B picks $b$, and C picks $c$.  Then;


Alice encrypts $M$ by computing $M^a \bmod p$
Alice decrypts $C$ by computing $M^{a^{-1} \bmod p-1} \bmod p$



If you go through the math, you'll see that:


Encryption and decryption are inverses of each other, e.g. $\operatorname{Dec}_a(\operatorname{Enc}_a(M)) = M$
It commutes just like you asked: $\operatorname{Enc}_b(\operatorname{Enc}_a(M)) = \operatorname{Enc}_a(\operatorname{Enc}_b(M))$, etc
No one can deduce anything by observing intermediate results (assuming that the prime is large enough to make the DLog and Diffie-Hellman problems hard)