The idea is, if specified, JAVA_PROCESS_NAME environment variable is specified by the user, the run-java.sh script passes the value as an argument to the final `exec` as a parameter to `-a`, e.g. exec -a "desired process name". If JAVA_PROCESS_NAME is not specified, then the default should be left as "java". This could probably be achieved with bash substring expansion, something like (untested)

exec -a "${JAVA_PROCESS_NAME:-java}" ...