Retrieve folder's name for Automator's shell script action
I'm assuming $1 is e.g. "/path/to/filename.VOB" so $current_path would be: /path/to

So, for $filename use filename="$(basename "$current_path")" placed after: current_path="$(dirname "$1")" and then ext=".VOB" afterwards. You can then change .VOB to other extensions as needed.

Thus, change "THIS_SHOULD_BE_THE_DIRECTORY_NAME.VOB" to "${filename}${ext}" as shown below:

#!/bin/bash

current_path="$(dirname "$1")"
filename="$(basename "$current_path")"
ext=".VOB"
cd "$current_path"

for f in "$@"
do
    /usr/local/Cellar/ffmpeg/4.1_1/bin/ffmpeg -i concat:"$(pipeize() { local OLDIFS="$IFS";IFS='|';echo "$*";IFS="$OLDIFS";}; pipeize *.VOB)" -c copy -map "0:v?" -map "0:a?" -map "0:s?" "${filename}${ext}"
done