WordPress with cloudfront , how to mask origin url

I'm facing an issue setting up wordpress with cloudfront.

I've set up all things fine, and it's working, but the problem is that when I send a request, the origin url is displayed in the address bar instead of the cname.

here is my origin vhost configuration :

<VirtualHost *:80>
        ServerAdmin admin@mydomain.com
        ServerName  origin.mydomain.com
        
        DocumentRoot /var/www/mysite.mydomain.com
        <Directory /var/www/mysite.mydomain.com>
                Options -Indexes MultiViews FollowSymlinks
                Options Indexes FollowSymLinks MultiViews
                #AllowOverride AuthConfig
                AllowOverride None
                Order allow,deny
                allow from all
        </Directory>
        <IfModule mod_headers.c>  
                Header unset Server  
                Header unset X-Pingback
                Header unset X-Powered-By  
                Header set Cache-Control "max-age=0, private, no-store, no-cache, must-revalidate"
        </IfModule>  
        ErrorLog ${APACHE_LOG_DIR}/mysite.mydomain.com/error.log


        CustomLog ${APACHE_LOG_DIR}/mysite.mydomain.com/access.log combined

</VirtualHost>

At the cloudfront side I have this for my distribution settings :

Domain Name : d7jz390azoodb9.cloudfront.net
    
Origin : origin.mydomain.net

CNAMEs : mysite.mydomain.com

I made DNS registristions so that :

origin.mydomain.com points to the_public_ip_address_of_myserver

mysite.mydomain.com is a cname of d7jz390azoodb9.cloudfront.net

All the above is working fine. My problem is that, when I enter this in my browser : http//mysite.mydomain.com, I get to my wordpress home page, and from the when I try to navigate, for example clicking on "login" (http://mysite.mydomain/wp-login.php), the url dispayed in my address bar at the top of my page is : http://origin.mydomain/wp-login.php instead, which can be then seen by any user.

If I type myself mysite.mydomain/wp-login.php directly in the browser, I get a Not found from cloudfront.

If I replace the ServerName in my vhost configuration by mysite.mydomain.com I get a Miss from cloudfront.

Do someone know to fix this, so that the url seeing by user always remain mysite.mydomain.com?

Thanks