Corrija as atribuições da matriz e altere o teste para um regex.
#!/bin/bash
FNAME="JACK"
LNAME="BLACK"
SEARCHNAME=()
SEARCHNAME+=("JACK-BLACK")
SEARCHNAME+=("JOHN-JAMES")
SEARCHNAME+=("CHRIS-TOPHER")
SEARCHNAME+=("JEN-NAY")
NAME="${FNAME}-${LNAME}"
if [[ "${SEARCHNAME[@]}" =~ $NAME ]]; then
echo "PASSED"
else
echo "FAILED"
fi
echo "SEARCH IN: ${SEARCHNAME[@]}"
echo "FOR NAME: ${NAME}"