Repeating the comment from MDEV-7567,

It remains unclear what was the role-model for log_slow_query_file_name.
We have a variety of patterns with similar meaning:
general_log_file
relay_log_info_file
wsrep_status_file
pid_file
log_error
log_bin_basename
innodb_buffer_pool_filename

but I couldn't find any %_file_name (maybe somewhere in optional plugins, those I didn't check).

So, maybe it should be just log_slow_query_file, like several existing _file's. Or even just log_slow_file, given the variable list

+---------------------------------+

| log_slow_min_examined_row_limit |

| log_slow_slave_statements |

| log_slow_query_time |

| log_slow_verbosity |

| log_slow_admin_statements |

| log_slow_disabled_statements |

| log_slow_query |

| log_slow_query_file_name |

| log_slow_rate_limit |

| log_slow_filter |

+---------------------------------+

Additionally, the help text for log-basename option contains a reference to this variable/option. It was already wrong before ("log-slow-query-log-file"), and will become even wronger now, so it should be fixed at the same time.

  --log-basename=name Basename for all log files and the .pid file. This sets

                      all log file names at once (in 'datadir') and is normally

                      the only option you need for specifying log files. Sets

                      names for --log-bin, --log-bin-index, --relay-log,

                      --relay-log-index, --general-log-file,

                      --log-slow-query-log-file, --log-error-file, and

                      --pid-file