Add element to rest end point.

rest.php

<?php
/**
 * Adds category names field to faqs post type.
 */
function add_category_names_to_api() {
	register_rest_field(
		'post', // post type.
		'category_names', // element.
		[
			'get_callback'    => __NAMESPACE__ . '\return_category_names'
		]
	);
}
add_action( 'rest_api_init', __NAMESPACE__ . '\add_category_names_to_api' );

/**
 * Populate post category names for reference.
 *
 * @param array $response Array of response properties so far.
 *
 * @return string list of comma-separated category names.
 */
function return_category_names( $response ) {
		global $post;

		// Shouldn't need this, but only make this update for posts.
		if ( 'post' !== $post->post_type ) {
			return '';
		}

		// Get terms.
		$category_list = [];
		$terms         = get_the_terms( $post, 'category' );

		if ( empty( $terms ) || is_wp_error( $terms ) ) {
			return '';
		}

		foreach( $terms as $term ) {
			$category_list[] = $term->name;
		}

		return implode( ', ', $category_list );
}