Unix was a kind of play word for Unique as an anti-thesis for Multics that latter was originally designed for modern multi-user and multi-process OS. Ironically as any real-world OS Unix eventually becomes multi-user system similar to Multics but the name stucked. Granted Unix has a very simple (as in simple as possible but no simpler) multi-user permission and security system that work reliably for many decades until now. Of all the organizations NSA actually even come up with a better replacement for the modern Unix permission and security model with SELinux, but most users just ignored and disabled SELinux although it's installed by default by many major Linux distros [1].

[1] SELinux is unmanageable; just turn it off if it gets in your way:

https://news.ycombinator.com/item?id=31176138