How to test my website through my paid provider?

Hi Croma. when your site is on the server, your website automatically go public. But you can block and limit visitor or search engine crawl to your web. Here are the options:

Don't share your web address to any of your friend. Not to social sharing too
to avoid search engine, do not use meta-tag and keyword. In Wordpress there's an option on Privacy to block from search engine. you can add meta tag after your web ready, 
Remove third party links from you web. usually from third party template, plugins, module, etc

or, if you want to be anonymous, you can try free host for temporary test your website. After you statisfy with your web, now you can publish on your own server. Don't forget to delete your temporary website too. :)