Чистое решение
$search_arr = explode(" ",$search);
$params = [];
$where = [];
foreach($search_arr as $word)
{
$where[] = "hospname like ?";
$params[] = "%$word%";
}
$query = "SELECT * FROM `hospitals` WHERE ".implode($where, " or ");
$sql = $conn->prepare($query);
$sql->bind_param(str_repeat('s', count($params)), ...$params);
$sql->execute();
$result = $sql->get_result();