Isolated or separated (from the host system). Both words will work when context is clear. Or it can confuse, when context was not specified, which is in my case.

What I actually meant is that I'd rather run an isolated (separated) process from other processes and the file-system space (and the other isolation features which cgroups are giving us), not meaning isolation from the host system.

With the cgroups/namespaces it's a process isolation (or separation, whatever wording you prefer). In the Linux kernel documentation they also use isolation wording. ;-)