This code works to update addon/extension plugin slugs during update from a premapped list. Code likely needs to be run in separate plugin/theme/mu-plugin/drop-in.

rename-plugins-after-update.php

<?php


/**
 * This code works to update addon/extension plugin slugs during update from a premapped list.
 *
 * Code likely needs to be run in separate plugin/theme/mu-plugin/drop-in.
 *
 * Tested Working On:
 * - Single Site: Updates Page - Singe Plugin.
 * - Single Site: Updates Page - Bulk Plugin Update.
 * - Single Site: AJAX Update from plugins page.
 * - Multisite: Network activated
 * - Multisite: Non network activated.
 *
 * Untested:
 * - 
 */

/**
 * Get list of plugins that need renaming.
 *
 * @return string[]
 */
function pum_get_renamed_plugin_map() {
	// Array of old plugin name => new plugin name.
	$renamed_plugin_map = [
		'pum-scheduling/pum-scheduling.php'     => 'popup-maker-scheduling/popup-maker-scheduling.php',
		'pum-geotargeting/pum-geotargeting.php' => 'popup-maker-geotargeting/popup-maker-geotargeting.php',
	];

	return $renamed_plugin_map;
}

/**
 * This function runs when WordPress completes its upgrade process.
 * It iterates through each plugin updated to see if it is included in our renamed plugin map.
 *
 * @param array $upgrader_object Array of information regarding the upgrade process.
 * @param array $options         Array of bulk item update data.
 */
function pum_monitor_plugin_udpates_for_renaming( $upgrader_object, $options ) {
	$renamed_plugin_map = pum_get_renamed_plugin_map();
	$renamed_plugins    = array_keys( $renamed_plugin_map );
	$_transient_data    = [];

	// If an update has taken place and the updated type is plugins and the plugins element exists.
	if ( 'update' === $options['action'] && 'plugin' === $options['type'] && isset( $options['plugins'] ) ) {
		// Iterate through the plugins being updated and check if ours is there.
		foreach ( $options['plugins'] as $plugin ) {
			if ( in_array( $plugin, $renamed_plugins, true ) ) {
				// Set a transient to record that our plugin has just been updated.
				$_transient_data[ $plugin ] = $renamed_plugin_map[ $plugin ];
			}
		}
	}

	if ( ! empty( $_transient_data ) ) {
		set_transient( 'pum_renamed_plugins', $_transient_data, DAY_IN_SECONDS );
	}
}
add_action( 'upgrader_process_complete', 'pum_monitor_plugin_udpates_for_renaming', 10, 2 );

/**
 * Forces reactivation of renamed plugin.
 *
 * @param string $plugin The plugin to check.
 * @param bool   $network_wide Whether to check for network wide activation.
 * @return void
 */
function force_activate_renamed_plugin( $plugin, $network_wide ) {
	$renamed_plugin_map = pum_get_renamed_plugin_map();

	if ( isset( $renamed_plugin_map[ $plugin ] ) ) {
		$renamed_plugin = $renamed_plugin_map[ $plugin ];

		// Deactivate the old plugin.
		if ( is_plugin_active( $plugin ) ) {
			deactivate_plugins( $plugin, true, $network_wide );
		}

		// Activate the new plugin.
		activate_plugin( $renamed_plugin, '', $network_wide );
	}
}

/**
 * This function reactivates plugins that have been renamed, without requireing user interaction.
 *
 * @return void
 */
function pum_rename_plugins() {
	$renamed_plugin_map = pum_get_renamed_plugin_map();

	// If we have no renamed plugins, return early.
	if ( empty( $renamed_plugin_map ) ) {
		return;
	}

	// Get the transient data.
	$_transient_data = get_transient( 'pum_renamed_plugins' );

	// If we have no transient data, return early.
	if ( empty( $_transient_data ) ) {
		return;
	}

	// Require neccesary functions if they don't exist.
	if ( ! function_exists( 'is_plugin_active' ) ) {
		include_once ABSPATH . 'wp-admin/includes/plugin.php';
	}

	// Foreach plugin in pum_renamed_plugins transient as $old_plugin => $new_plugin.
	foreach ( $_transient_data as $old_plugin => $new_plugin ) {
		// 1. If the old file exists & new file does not, the migration we're fixing didn't occur, unset & continue.
		if ( file_exists( WP_PLUGIN_DIR . '/' . $old_plugin ) && ! file_exists( WP_PLUGIN_DIR . '/' . $new_plugin ) ) {
			unset( $_transient_data[ $old_plugin ] );
			continue;
		}

		// 2. Check if the old plugin was network active.
		$network_wide = is_multisite() && is_plugin_active_for_network( $old_plugin );

		// 3. If is multisite & not network wide, loop over every site and force activate the new plugin. Else just force activate the new plugin.
		if ( is_multisite() && ! $network_wide ) {
			$sites = get_sites();

			foreach ( $sites as $site ) {
				switch_to_blog( $site->blog_id );
				// Only force activate if the plugin was active on this site before.
				if ( is_plugin_active( $old_plugin ) ) {
					force_activate_renamed_plugin( $old_plugin, false );
				}
				restore_current_blog();
			}
		} else {
			force_activate_renamed_plugin( $old_plugin, $network_wide );
		}

		// 4. Remove $old_plugin from pum_renamed_plugins transient.
		unset( $_transient_data[ $old_plugin ] );
	}

	if ( empty( $_transient_data ) ) {
		delete_transient( 'pum_renamed_plugins' );
	} else {
		set_transient( 'pum_renamed_plugins', $_transient_data, DAY_IN_SECONDS );
	}
}

add_action( 'init', 'pum_rename_plugins' );

Updated with handling for multisite with non-network_wide activation.

Updated again with minor tweaks and full support for non-network wide activations on multi-site.