Forking Linux would involve taking on a huge maintenance burden, so everyone just uses it, though often basing on an older version and/or with some custom patches. That is typically how healthy open source stuff works.

Companies DO put brand names on systems built on top of Linux (or a BSD) all the time though, often ones that don’t make it obvious that’s what it is. ChromeOS and Android are both Linux based, but Android doesn’t ship most of the UNIX-y parts that are typically layered on top, and instead uses their own (also largely open source) components. ChromeOS is actually a fairly close relative of Gentoo with a few custom pieces.

Google has their own internal project for a kernel called Fuchsia, and it’s really interesting modern OS development that they’ve assembled a bunch of experts to work on… But it’s increasingly unclear if they plan to deploy it on customer facing products.

A ton of appliance type devices are basically very tiny custom Linux systems, often assembled with tools like Yocto. A lot if the vendors who sell components to go into said devices contribute code and/or money to Linux and Yocto, in order to make their products more attractive to device builders and avoid having to make and maintain their own tooling.

Most consumer routers are basically Linux (usually with a minimal userland like BusyBox), often essentially shitty old customized versions of OpenWRT. Sony alpha cameras? Customized Linux. Off on the BSD side, CellOS and OrbisOS that the PS3 and PS4 run, respectively are modified FreeBSD. Open Source OSes and tooling are everywhere because making, maintaining, and building tooling and developer support for an OS that runs on especially relatively large modern computers is a big, hard project, so very few entities try to do it themselves.