Magento2 – Custom Customer Attribute Value Not Saving During Registration

You can do this by observer.

SR/StackExchange/etc/frontend/events.xml

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:Event/etc/events.xsd">
    <event name="customer_register_success">
        <observer name="sr_customer_account_createPost" instance="SR\StackExchange\Observer\CustomerRegisterSuccess" />
    </event>
</config>

SR/StackExchange/Observer/CustomerRegisterSuccess.php

namespace SR\StackExchange\Observer;

use Magento\Framework\Event\ObserverInterface;
use Magento\Framework\Event\Observer;
use Magento\Customer\Api\CustomerRepositoryInterface;

class CustomerRegisterSuccess implements ObserverInterface
{
    /** @var CustomerRepositoryInterface */
    protected $customerRepository;

    /**
     * @param CustomerRepositoryInterface $customerRepository
     */
    public function __construct(
        CustomerRepositoryInterface $customerRepository
    ) {
        $this->customerRepository = $customerRepository;
    }

    /**
     * Manages redirect
     */
    public function execute(Observer $observer)
    {
        $accountController = $observer->getAccountController();
        $customer = $observer->getCustomer();
        $request = $accountController->getRequest();
        $customer_number = $request->getParam('customer_number');
        $customer->setCustomAttribute('customer_number', $customer_number);
        $this->customerRepository->save($customer);
    }
}

NB: here 'customer_number' is custom attribute

I have got the solution

protected $customer;

protected $customerFactory;

public function __construct(
    \Magento\Customer\Model\Customer $customer,
    \Magento\Customer\Model\ResourceModel\CustomerFactory $customerFactory
)
{
    $this->customer = $customer;
    $this->customerFactory = $customerFactory;
}

...
...

$customerId = "1";
$customer = $this->customer->load($customerId);
$data = "customer attribute value";
$customerData = $customer->getDataModel();
$customerData->setCustomAttribute('customer_attribute_code',$data);
$customer->updateData($customerData);
$customerResource = $this->customerFactory->create();
$customerResource->saveAttribute($customer, 'customer_attribute_code');