Modify the Theme My Login widget title and user links displayed when using the Memberlite theme (https://memberlitetheme.com).

memberlite_modify_tml_widget.php

<?php //Do not copy this PHP tag into your code.
/**
  * Modify the Theme My Login widget title and user links displayed when using the Memberlite theme
  * https://memberlitetheme.com
  *
  * This code recipe changes the widget's title to "Welcome, Display_Name" for logged in users. 
  *
  * It also removes the default user links included in the widget and replaces it with
  * the same links as your "Members" menu as assigned under Appearance > Menus when using Memberlite.
  * under Memberships > Pages.
  *
  * Add this code below to a plugin for theme customizations.
  */

//Replace the Theme My Login widget's title with "Welcome, Display_Name" for logged in users. 
function modify_tml_widget_title( $title, $instance, $id_base ) {
	global $current_user, $pmpro_pages;
	if ( is_user_logged_in() && $id_base === 'theme-my-login' ) {
		$user_ID = $current_user->ID;
		if ( ! empty( $pmpro_pages ) ) {
			$account_page      = get_post( $pmpro_pages['account'] );
			$user_account_link = '<a href="' . esc_url( pmpro_url( 'account' ) ) . '">' . preg_replace( '/\@.*/', '', $current_user->display_name ) . '</a>';
		} else {
			$user_account_link = '<a href="' . esc_url( admin_url( 'profile.php' ) ) . '">' . preg_replace( '/\@.*/', '', $current_user->display_name ) . '</a>';
		}
		$title = sprintf( __( 'Welcome, %s', 'memberlite' ), $user_account_link );
	}
	return $title;
}
add_filter( 'widget_title', 'modify_tml_widget_title', 10, 3 );

// Remove all user_links added via the Theme My Login widget's default logic.
function hide_tml_widget_user_links( $links ) {
	$links = '';
	return $links;
}
add_filter ('tml_widget_user_links', 'hide_tml_widget_user_links' );

// Display the "Members" menu as assigned under Appearance > Menus when using Memberlite.
function show_member_menu_tml_widget_user_panel( ) {
	global $current_user;
	$user_ID = $current_user->ID;
	if ( $user_ID ) {
		$member_menu_defaults = array(
			'theme_location'  => 'member',
			'container'       => 'nav',
			'container_id'    => 'member-navigation',
			'container_class' => 'member-navigation',
			'fallback_cb'     => 'memberlite_member_menu_cb',
			'items_wrap'      => '<ul id="%1$s" class="%2$s">%3$s</ul>',
		);
	} else {
		$member_menu_defaults = array(
			'theme_location'  => 'member-logged-out',
			'container'       => 'nav',
			'container_id'    => 'member-navigation',
			'container_class' => 'member-navigation',
			'fallback_cb'     => 'memberlite_member_menu_cb',
			'items_wrap'      => '<ul id="%1$s" class="%2$s">%3$s</ul>',
		);
	}
	wp_nav_menu( $member_menu_defaults );
}
add_action( 'tml_widget_user_panel', 'show_member_menu_tml_widget_user_panel' );