C doesn't even need namespaces for this, a simple stdc_ prefix for stdlib functions and types would also work (see C23 stdbit.h, I hope this won't be an outlier).
Yes, but we can't simply port C++ namespaces over because this requires symbol name mangling. C could be using 'namespace prefixes' instead with something like 'usingprefix stdc_', this wouldn't require changes to the symbol format, and would provide most of the features of C++ namespaces.