Custom markup for the comment form

Yeah this should be possible using the comment_form_default_fields filter, like so:

apply_filters( 'comment_form_default_fields', $fields );

$fields = array( 'name' => '<section class="form-group">
    <input type="text" class="form-control" id="name" placeholder="Your name" />
</section>'
);

Just remember to add any other fields that you want to add into that array too.