You are passing an array of arrays to implode
function. Here is a little deviation of your code, that should get you to the same result:
$full_array = array();
foreach ($RespondentsResultSetArray as $key) {
echo $key["Firstname"] . ' ' . $key["Lastname"] . ', ';
array_push($full_array,$key["Firstname"]);
array_push($full_array,$key["Lastname"]);
}
echo implode(', ',$full_array);
Also, for the future, try to chose smaller names for your variables, and use lowercase for your variable names and array index.