My solution (works with multiple identical names and provides feedback on no results)

var userInput;
var recordsToReturn = '';

function print(message) {
    var outputDiv = document.getElementById('output');
    outputDiv.innerHTML = message;
}

while ( true ) {
    recordsToReturn = '';
    userInput = prompt('Search for student first name. Press cancel to stop');
    if ( userInput === null ) {
        break;
    }
    for ( i=0; i < students.length; i++ ) {
        if ( students[i].name.toUpperCase() === userInput.toUpperCase() ) {
            recordsToReturn += 
                '<p><strong>Student name: ' + students[i].name +
                '</strong></p> <p>Track: ' + students[i].track +
                '</p> <p>Achievements: ' + students[i].achievements +
                '</p> <p>Points: ' + students[i].points + '</p></br>'
            ;
        }
    }
    if ( recordsToReturn === '' ) {
        recordsToReturn = 'No student "' + userInput + '" was found.';
    }
    print(recordsToReturn);
}