Attribute terms description not showing

It depends on what function is generating that dropdown. It’s reasonable to expect it to call get_terms() at some point. You can use the “get_terms” filter to alter the data returned, setting each description as the term’s name property. I don’t think doing so will affect any upstream functions, but this is an untested idea.

The filter’s docs page is https://developer.wordpress.org/reference/hooks/get_terms/
It is applied here, but absolutely do not change that code. It’s just FYI.

Filtered values are altered through filter hooks, whose code can be added to a child theme’s functions.php or added to a custom plugin. Creating a simple plugin is a bit easier than making a child theme. Neither are difficult to do.

I don’t normally code for forum members like this, but I seem to have some extra time on my hands. Create a new plain text file and add this code:

<?php
/**
 * Plugin Name: Description to Name
 * Description: Copies term descriptions to the name field for display purposes
 * Author: bcworkz
 * Version: 0.10 beta
 */

// Define targeted taxonomy here
define('BCW_TAX', 'my-taxonomy');

add_filter('get_terms', function( $terms, $tax, $args ) {
	// check if $terms is in a format our code can work with
	if ( BCW_TAX == $tax[0] && 'all'== $args['fields'] && NULL == $args['object_ids']) {
		$copy = array();
		foreach ( $terms as $term) {
			$term->name = $term->description;
			$copy[] = $term;
		}
		return $copy;
	}
	return $terms;
 }, 10, 3 );

Change 'my-taxonomy' to whatever your taxonomy name is in the define() line. Save the file as “description-to-name.php”. Upload via FTP to /wp-content/plugins/ on your server. Log into your WP site and activate the “Description to Name” plugin.

I did some very limited testing to ensure there are no blatant errors. There may be unanticipated side effects I’ve not anticipated.