Also the term slug should never change, unlike the term name which is easy to change. Even the slug can be changed but it is more difficult.
I would create a custom field on the terms for setting the color and then I’d code this into the template to ensure that I don’t have to revisit the css every time someone adds or changes a term.
$color = get_field('color_field_name', $term);
//.....
<span class="cat-icon" style="color: <?php echo $color; ?>"><?php echo $icon; ?></span>
