There are no company tax numbers in Estonia.
Your company registration code is enough in Estonia for all public and private services.
If a foreign service provider requests you to present company unique taxpayer number (TIN), then just present your company registration code.
If a service provider asks for company VAT registration number, you should know that it is not mandatory to have a VAT registration in Estonia if you are below the annual treshold of taxable supply (currently 40 000 euros). Therefore it should not be compulsory to access any service with your Estonian company.
To register your company for VAT even if your supplies have not exceeded 40 000 euros annually, please continue to this article.