$_SESSION: Undefined Index - php

Question

I'm creating a booking site for meeting rooms.
I have done the sql query to search for free rooms according to the time and date chosen.
This is working. I display the free rooms (in a while loop) in cards with datas from the query.
<?php
if (isset($_POST['submit'])) {
echo '<main role="main">
<div class="card-columns">';
require_once 'connexion_BD.php';
$res_date = $_POST['res_date'];
$res_date = date("Y-m-d", strtotime($res_date));
$res_horaire_id = $_POST['res_horaire'];
$_SESSION['res_date'] = $_POST['res_date'];
$_SESSION['res_horaire'] = $_POST['res_horaire'];
$sql = "SELECT sal_nom, sal_nb_place, sal_notes
FROM salle
WHERE sal_id NOT IN (SELECT res_sal_id FROM reservation WHERE res_date = :res_date AND res_horaire_id = :res_horaire_id)";
$requete = $db->prepare($sql);
$requete->bindValue(':res_date', $res_date);
$requete->bindValue(':res_horaire_id', $res_horaire_id);
$requete->execute();
$i=0;
while ($row = $requete->fetch()) {
$tab_sal_nom[0+$i] = $row['sal_nom'];
$tab_sal_nb_place[0+$i] = $row['sal_nb_place'];
$tab_sal_notes[0+$i] = $row['sal_notes'];
?>
<div class="card bg-light">
<img class="card-img-top" <?php echo 'src="img/salle_reunion_'. rand(1, 8) .'.jpg"' ?> alt="Salle de réunion">
<div class="card-body">
<h5 class="card-title">Salle <?php echo $tab_sal_nom[0+$i]; ?></h5>
<p class="card-text">Salle disposant de <?php echo $tab_sal_nb_place[0+$i]; ?> places.</p>
<p class="card-text"><small class="text-muted">Informations de salle : <?php echo $tab_sal_notes[0+$i]; ?></small></p>
<form action="confirm_resa.php" method="POST">
<button class="btn btn-outline-primary float-right" style="margin-bottom: 15px;" name=<?php echo '"reserver_'.$tab_sal_nom[0+$i].'"'?> type="submit">Réserver</button>
</form>
</div>
</div>
<?php
$i = $i + 1;
}
}
?>
Now here's my problem, I want to know which room name the user choose to store the info in a $_SESSION['sal_choix'], so, I look at the submit button named <?php echo '"reserver_'.$tab_sal_nom[0+$i].'"'?> (equals to reserver_Daum, reserver_Majorelle, reserver_Galle, reserver_Corbin etc...)
My idea was to look with some if:
if (isset($_POST['reserver_Daum'])) $_SESSION['sal_choix'] = "Daum";
elseif (isset($_POST['reserver_Galle'])) $_SESSION['sal_choix'] = "Galle";
etc...
But that's not working, cause in the confirm_resa.php, $_SESSION['sal_choix'] is: undefined index
It's not a session problem because two other : $_SESSION['res_date'] and $_SESSION['res_horaire'] are sets.
I'm pretty sure the problem is in the if(isset($_POST[])) but I can't see it...
help pls!