How to make your replacement for a C language Google-able: name it after an API for a C language: Carbon was one of two primary C-based application programming interfaces (APIs) developed by Apple for the macOS (formerly Mac OS X and OS X) operating system. Compare also keywords or key terms: Carbon will be built on a foundation on modern programming principles, including a generics system, that would remove the need…
Carbon API is so old that this pretty much isn't issue. You have to google explicitely for "Carbon API" for it to show up. Whether even now, "carbon programming" or "carbon code" give results for Carbon language - and some other non-c++ libs named Carbon. Even "carbon" by itself gives me some Carbon language links.
Carbon (the Mac API) only existed to enable developers to more easily port Mac 8/9 applications to OS X, which was over 20 years ago. The Carbon API was officially discontinued in 2019 with Catalina.
The Carbon API served its purpose, it's now officially "dead", so I agree - I don't see much of an issue with giving a new technology the same name.