As discussed in the WordPress Support Forums, in some instances, it’s easier to develop an array which stores the value value.
To group the checkboxes, I simply copied the same format from the Discussion settings page to get my expected result: a group of checkboxes that are formatted using WordPress’ native style. Here’s a good template to work off of:
<div class="wrap">
<h1>Profile Settings</h1>
<form method="post" action="action_here">
<table class="form-table">
<tbody>
<tr>
<th scope="row">Personal Options</th>
<td>
<fieldset>
<legend class="screen-reader-text"><span>Personal Options</span></legend>
<label for="rich_editing">
<input name="rich_editing" type="checkbox" value="rich_editing" />
Visual Editor</label>
<br>
<label for="admin_color">
<input name="admin_color" type="checkbox" value="admin_color" />
Admin Color Scheme</label>
<br>
<label for="comment_shortcuts">
<input name="comment_shortcuts" type="checkbox" value="comment_shortcuts" />
Keyboard Shortcuts</label>
<br>
<label for="admin_bar_front">
<input name="admin_bar_front" type="checkbox" value="admin_bar_front" />
Toolbar</label>
<br>
</fieldset>
</td>
</tr>
<tr>
<th scope="row">Name</th>
<td>
<fieldset>
<legend class="screen-reader-text"><span>Name</span></legend>
<label for="first_name">
<input name="first_name" type="checkbox" value="first_name" />
First Name</label>
<br>
<label for="last_name">
<input name="last_name" type="checkbox" value="last_name" />
Last Name</label>
<br>
<label for="nickname">
<input name="nickname" type="checkbox" value="nickname" />
Nickname</label>
<br>
<label for="display_name">
<input name="display_name" type="checkbox" value="display_name" />
Display Name</label>
<br>
</fieldset>
</td>
</tr>
</tbody>
</table>
<?php submit_button(); ?>
</form>
</div>
Result
