This Wordpress plugin adds custom features and modifications to the Ultimate Member plugin family.

UltimateMembersMods

<?php
/**
 * Plugin Name:  Ultimate Member Modifications
 * Plugin URI:   http://geminilabs.io
 * Description:  This plugin adds custom features and modifications to the Ultimate Member plugin family.
 * Version:      1.0.0
 * Author:       Gemini Labs
 * Author URI:   http://geminilabs.io
 * License:      MIT License
 */

class UltimateMembersMods
{
	/**
	 * Instantiate the class
	 *
	 * @return void
	 */
	public function __construct()
	{
		// Allows a user to set their Display Name in the Account settings
		add_action( 'um_after_account_general',               [ $this, 'addDisplayNameFieldToAccount' ] );

		// Adds new post notifications to followers
		add_filter( 'um_notifications_core_log_types',        [ $this, 'notificationsAddTypes' ] );
		add_filter( 'um_notifications_get_icon',              [ $this, 'notificationsAddIcons' ], 10, 2 );
		add_action( 'transition_post_status',                 [ $this, 'notificationsLogNewPost' ], 10, 3 );
	}

	/**
	 * Add the Display Name field to account settings
	 *
	 * @return void
	 */
	public function addDisplayNameFieldToAccount()
	{
		global $ultimatemember;

		$fields = $ultimatemember->builtin->get_specific_fields( 'display_name' );

		foreach( $fields as $key => $data ) {
			echo $ultimatemember->fields->edit_field( $key, $data );
		}
	}

	/**
	 * Add custom notification types
	 *
	 * @param array $array
	 *
	 * @return array
	 */
	public function notificationsAddTypes( $array )
	{
		$array['user_post'] = array(
			'title'        => __( 'New user post', 'geminilabs' ),
			'template'     => '<strong>{member}</strong> has created a new post: <strong>{post_title}</strong>',
			'account_desc' => __( 'When a member you follow publishes a new post', 'geminilabs' ),
		);

		return $array;
	}

	/**
	 * Add custom notification icons
	 *
	 * @param string $output
	 * @param string $type
	 *
	 * @return string
	 */
	public function notificationsAddIcons( $output, $type )
	{
		if( $type == 'user_post' ) {
			$output = '<i class="um-faicon-pencil-square-o" style="color: #9A86FF"></i>';
		}

	    return $output;
	}

	/**
	 * Log notifications for new posts
	 *
	 * @param string  $new_status
	 * @param string  $old_status
	 * @param WP_Post $post
	 *
	 * @return void
	 */
	public function notificationsLogNewPost( $new_status, $old_status, $post )
	{
		if( !defined( 'ultimatemember_version' )
			|| !defined( 'um_notifications_version' )
			|| !defined( 'um_followers_version' )
			|| !function_exists( 'um_user' )
			|| !function_exists( 'um_fetch_user' )
			|| !function_exists( 'um_get_avatar_url' )
			|| $new_status == $old_status
			|| $new_status != 'publish' ) {
			return;
		}

		global $ultimatemember, $um_followers;

		$author    = $post->post_author;
		$followers = $um_followers->api->followers( $author );

		if( is_array( $followers ) ) {
			um_fetch_user( $author );

			$new  = [];
			$vars = [];

			$vars['member']           = um_user( 'display_name' );
			$vars['photo']            = um_get_avatar_url( get_avatar( $author, 40 ) );
			$vars['post_title']       = $post->post_title;
			$vars['notification_uri'] = get_permalink( $post->ID );

			array_walk( $followers, function( $key ) use( &$new ) {
				$new[] = $key[ key( $key ) ];
			} );

			// we only want unique user IDs
			$followers = array_keys( array_flip( $new ) );

			$this->storeNotifications( $followers, 'user_post', $vars );
		}
	}

	/**
	 * Store notifications for multiple users
	 *
	 * @param array  $users
	 * @param string $type
	 * @param array  $vars
	 *
	 * @return void
	 */
	public function storeNotifications( $users, $type, $vars = [] )
	{
		global $wpdb, $um_notifications;

		$users = $this->usersWithNotificationEnabled( $type, $users );

		if( !$users ) {
			return;
		}

		$content = $um_notifications->api->get_notify_content( $type );

		if( is_array( $vars ) ) {
			foreach( $vars as $key => $var ) {
				$content = str_replace( '{'.$key.'}', $var, $content );
			}
		}

		$content = implode( ' ', array_unique( explode( ' ', $content ) ) );

		if( $vars && isset( $vars['photo'] ) ) {
			$photo = $vars['photo'];
		}
		else {
			if( function_exists( 'um_get_default_avatar_uri' ) ) {
				$photo = um_get_default_avatar_uri();
			}
			else {
				// @todo fallback to wordpress method
				$photo = '';
			}
		}

		if( $vars && isset( $vars['notification_uri'] ) ) {
			$url = $vars['notification_uri'];
		}

		$table_name = $wpdb->prefix . "um_notifications";
		$followers  = implode( ',', $users );
		$time       = current_time( 'mysql' );

		// 1. Look for similar logs
		$results = $wpdb->get_results(
			$wpdb->prepare(
				"SELECT * FROM {$table_name} WHERE user IN ({$followers}) AND type='%s' AND content='%s' ORDER BY time DESC",
				$type,
				$content
			)
		);

		// 2. Update any found similar logs
		if( !empty( $results ) ) {

			array_walk( $results, function( $result ) use( &$notification_updates ) {
				$notification_updates[] = $result->user;
			} );

			$updates = implode( ',', $notification_updates );

			$wpdb->check_current_query = false;

			$wpdb->query(
				$wpdb->prepare(
					"UPDATE {$table_name} " .
					"SET status = 'unread', time = '%s' " .
					"WHERE user IN ({$updates}) AND type='%s' AND content='%s'",
					$time,
					$type,
					$content
				)
			);

			$users = array_diff( $users, $notification_updates );
		}

		// 3. Insert the rest of the logs
		if( !empty( $users ) ) {

			foreach( $users as $user_id ) {
				$rows[] = "('{$time}',{$user_id},'unread','{$photo}','{$type}','{$url}','{$content}')";
			}

			$values = implode( ',', $rows );

			$wpdb->check_current_query = false;

			$wpdb->query(
				"INSERT INTO {$table_name} (time,user,status,photo,type,url,content) VALUES{$values}"
			);
		}
	}

	/**
	 * Filter users that have the notification enabled
	 *
	 * @param string $key
	 * @param array  $users
	 *
	 * @return array|false
	 */
	public function usersWithNotificationEnabled( $key, $users )
	{
		if( is_array( $users ) && um_get_option( 'log_'.$key ) ) {

			$array = [];

			foreach( $users as $i => $user_id ) {

				$prefs = get_user_meta( $user_id, '_notifications_prefs', true );

				if( $prefs && isset( $prefs[ $key ] ) && !$prefs[ $key ] ) {
					unset( $users[ $i ] );
				}
			}

			// re-index array after unset
			return array_values( $users );
		}

		return false;
	}
}

new UltimateMembersMods;

This gist is over 5 years old. No idea if it works or not.

I managed to fix it :) Other than commenting out the addDisplayNameFieldToAccount part, I had to change these two lines:

		//$followers = $um_followers->api->followers( $author );
		$followers = UM()->Followers_API()->api()->followers( $author );
		//$content = $um_notifications->api->get_notify_content( $type );
		$content = UM()->Notifications_API()->api()->get_notify_content( $type );