使用PHP将HTML表格保存到文本文件中

I am trying to make a sign-up form where a user enters their name into a time slot. Then the names are saved into a text file but it is not being saved into the text file.

HTML form party

<form action="writeit.php" method="POST" name="nameform">
<table style="width:20%">
<tr>
<th>Time</th>
<th colspan="2">Name</th>
</tr>
<tr>
<td>8:00am</td>
<td><input type="text" name="name" id="name"></td>
</tr>
<tr>
<td>9:00am</td>
<td><input type="text" name="name" id="name"></td>
</tr>
<tr>
<td>10:00am</td>
<td><input type="text" name="name" id="name"></td>
</tr>
<tr>
<td>11:00am</td>
<td><input type="text" name="name" id="name"></td>
</tr>
<tr>
<td>12:00pm</td>
<td><input type="text" name="name" id="name"></td>
</tr>
<tr>
<td>1:00pm</td>
<td><input type="text" name="name" id="name"></td>
</tr>
<tr>
<td>2:00pm</td>
<td><input type="text" name="name" id="name"></td>
</tr>
<tr>
<td>3:00pm</td>
<td><input type="text" name="name" id="name"></td>
</tr>
<tr>
<td>4:00pm</td>
<td><input type="text" name="name" id="name"></td>
</tr>
<tr>
<td>5:00pm</td>
<td><input type="text" name="name" id="name"></td>
</tr>
</table>
<br></br>
<input type="submit" name="submit" value="Save">
</form>

the writeit.php file

<?php

$names = $_POST['name'];
$filename = "signup.txt";
$file = fopen($filename, "a");
fwrite($file, $names);
fclose($file);

?>