As this plugin support multiple recipients, showing other users name is little confusing as there may have more than one receiver. If you support to send message to only one receiver then you can follow following approach.

If you want to show other users avatar add following code in your theme’s (child theme you are using one) functions.php

add_filter( 'fep_remove_own_avatar_from_messagebox', '__return_true' );

If you want to show other user name add following code in your theme’s (child theme you are using one) functions.php

add_action( 'fep_message_table_column_content_author', function(){
	$participants = fep_get_participants( fep_get_the_id() );
	foreach( $participants as $participant ) {
		if ( get_current_user_id() != $participant ) {
			?><span class="fep-message-author"><?php echo fep_user_name( $participant ); ?></span><span class="fep-message-date"><?php echo fep_get_the_date( 'mgs_last_reply_time' ); ?></span><?php
			break;
		}
	}
});

Recipients name never shows in that page as multiple recipients issue. If i get a better idea how to show the name including multiple recipients case, i will add that in future version.

If you want now you can edit view-message-heads.php template following https://www.shamimsplugins.com/docs/front-end-pm-pro/customization-front-end-pm-pro/change-templates/