Only require First Name, Last Name and Email address - works best for Free membership checkouts and when your paid checkout does not require Billing Address.

simple_checkout_name_email_only_signup.php

<?php
/**
 * Only Username and Email address to create user.
 * Name Fields only on Profile not checkout page
 * This recipe requires Paid Memberships Pro and the Register Helper Add On.
 */

/**
 * Hide the Account Information Section
 */
function simple_checkout_hide_account_information_section( $skip_account_fields, $current_user ) {
	if ( empty( $current_user->ID ) ) {
		$skip_account_fields = 1;
	}
	return $skip_account_fields;
}
add_filter( 'pmpro_skip_account_fields', 'simple_checkout_hide_account_information_section', 10, 2 );

/**
 * Don't load any of the Billing Information fields.
 */
function simple_checkout_remove_billing_address_fields( $include ) {
	return false;
}
add_filter( 'pmpro_include_billing_address_fields', 'simple_checkout_remove_billing_address_fields' );

/**
 * Unset required account fields, we'll use Register Helper to require our new fields.
 */
function my_required_user_fields( $pmpro_required_user_fields ) {
	unset( $pmpro_required_user_fields['username'] );
	unset( $pmpro_required_user_fields['password'] );
	unset( $pmpro_required_user_fields['password2'] );
	unset( $pmpro_required_user_fields['bconfirmemail'] );
	
	return $pmpro_required_user_fields;
}
add_filter( 'pmpro_required_user_fields', 'my_required_user_fields', 10, 2);

/**
 * Register Helper Required Fields
 */
function simple_checkout_name_email_only_signup_pmprorh_init() {
	//don't break if Register Helper is not loaded
	if ( ! function_exists( 'pmprorh_add_registration_field' ) ) {
		return false;
	}
	
	//define the fields
	$fields = array();
	$fields[] = new PMProRH_Field(
		'username',
		'text',
		array(
			'label' => 'User Name - only half-width alphanumeric characters cannot be spaced',
			'html_attributes' => array( 'placeholder' => 'only half-width alphanumeric characters cannot be spaced' ),
			'hint' => 'Hint can go here.',
			'profile' => false,
			'required' => true
		)
	);

	$fields[] = new PMProRH_Field(
		'bfirstname',
		'text',
		array(
			'label' => 'First Name',
			'profile' => "only",
			'required' => true
		)
	);
	$fields[] = new PMProRH_Field(
		'blastname',
		'text',
		array(
			'label' => 'Last Name',
			'profile' => "only",
			'required' => true
		)
	);
	$fields[] = new PMProRH_Field(
		'bemail',
		'text',
		array(
			'label' => 'Email Address',
			'profile' => true
		)
	);
	$fields[] = new PMProRH_Field(
		'bconfirmemail_copy',
		'hidden',
		array(
			'label' => '&nbsp;',
			'value' => '1',
		)
	);

	pmprorh_add_checkout_box( 'account', 'Account Information');

	//add the fields into a new checkout_boxes are of the checkout page
	foreach ( $fields as $field ) {
		pmprorh_add_registration_field(
			'account',
			$field
		);
	}
}
add_action( 'init', 'simple_checkout_name_email_only_signup_pmprorh_init' );