Filter the user nicename to use a sanitized first-name-last-name format.

my_set_safe_user_nicename.php

<?php
/**
 * Filter the user nicename to use a sanitized first-name-last-name format.
 */
function my_set_safe_user_nicename( $nicename ) {
	if ( ! isset( $_POST['first_name'] ) || ! isset( $_POST['last_name'] ) ) {
		return $nicename;
	}

	$first_name = sanitize_text_field( $_POST['first_name'] );
	$last_name  = sanitize_text_field( $_POST['last_name'] );

	if ( empty( $first_name ) && empty( $last_name ) ) {
		return $nicename;
	}

	$base_nicename = sanitize_title( $first_name . '-' . $last_name );
	$new_nicename  = $base_nicename;
	$counter       = 1;

	// Ensure uniqueness.
	while (
		username_exists( $new_nicename ) ||
		get_user_by( 'slug', $new_nicename )
	) {
		$new_nicename = $base_nicename . '-' . $counter;
		$counter++;
	}

	return $new_nicename;
}
add_filter( 'pre_user_nicename', 'my_set_safe_user_nicename' );