Basic example of using a custom callback function for a PMPro User Field created with code.

save-function-custom-callback.php

<?php
// Create a registration form field with a custom callback
function my_pmpro_user_field_example_save_function() {
	// Don't break if PMPro is out of date or not loaded.
	if ( ! function_exists( 'pmpro_add_user_field' ) ) {
		return false;
	}
	// define the fields
	$fields = array();
	// Basic Text Field Example
	$fields[] = new PMPro_Field(
		'my_field_name', // input field name, used as meta key
		'text',          // field type
		array(
			'label'         => 'My Field Label', // field label
			'profile'       => true,            // display on user profile
			'save_function' => 'my_custom_callback_function', // use a custom callback function
		)
	);

	foreach ( $fields as $field ) {
		pmpro_add_user_field(
			'checkout_boxes', // location on checkout page
			$field            // PMPro_Field object
		);
	}
}
add_action( 'init', 'my_pmpro_user_field_example_save_function' );

// Custom callback function
function my_custom_callback_function( $field_value ) {
	// Do something
}

This recipe is included in the blog post on "How to Use a Custom Callback Function For User Profile or Registration Fields" at Paid Memberships Pro here: https://www.paidmembershipspro.com/custom-callback-function-save-user-registration-profile-fields/