The C-like languages, plus Pascal, Ada, and others, are part of the Algol superfamily of languages.

"Family" and "superfamily" aren't well defined, in the way that it is for biological taxonomy, but I think it's intuitively clear enough for this discussion.

The Python family includes the various CPython language implementations, plus JPython/Jython, Iron Python, and PyPy, as well as wider-away dialects like Cython. At some point it's part of the Python superfamily.

What's the name for the family of languages which includes Perl 6 and Raku?

I think "Perl-like" includes Perl 4, 5, and 6, Raku, as well as (further away), Ruby.

I think Perl 6 and Raku are parts of the Perl 6 family, following the usual tradition of naming language families after the first instance in that family. (It isn't always that, see https://wiki.c2.com/?WirthLanguages ).

What would you suggest as the family name for Raku and Perl 6 which excludes the more distant members of the family, like Perl 5?

Delphi is an Object Pascal, for example.