That practice SEEMS to be very rare—we can't find any examples other than the misuse of the name “Linux”. Normally an operating system is developed as a single unified PROJECT, and the DEVELOPERS choose a name for the system as a whole. The kernel usually does not have a name of its own—instead, people say “the kernel of such-and-such” or “the such-and-such kernel”.

Because those two constructions are USED synonymously, the expression “the Linux kernel” can easily be misunderstood as meaning “the kernel of Linux” and implying that Linux must be more than a kernel. You can AVOID the possibility of this misunderstanding by saying or writing “the kernel, Linux” or “Linux, the kernel.”

That practice seems to be very rare—we can't find any examples other than the misuse of the name “Linux”. Normally an operating system is developed as a single unified project, and the developers choose a name for the system as a whole. The kernel usually does not have a name of its own—instead, people say “the kernel of such-and-such” or “the such-and-such kernel”.

Because those two constructions are used synonymously, the expression “the Linux kernel” can easily be misunderstood as meaning “the kernel of Linux” and implying that Linux must be more than a kernel. You can avoid the possibility of this misunderstanding by saying or writing “the kernel, Linux” or “Linux, the kernel.”