I don't think there is a name for either set of naming conventions.
The naming conventions in the C and C++ standards are different, though faintly related.
In particular, in the C library, no function or macro name contains an underscore (AFAICR), unlike the C++ library.
Most of the C library naming convention was controlled by precedent; it standardized existing practice (as of about 1984), with remarkably few inventions (locale handling via <locale.h>
being the main one).
The C++ library was based on precedent too - but a different set of precedents, and I think it is arguable that the STL was not in as widespread use prior to its adoption by the standard as the functions in the C library were.