About a year ago, the director hired a programmer from another country to develop a website for our company. Since the management lacks understanding of website creation and hosting, the programmer took care of everything. However, now we are facing a problem as this person is unreachable - not responding to calls or Skype messages. We are unsure if the domain lease has been paid or not, and there is a risk that the website might stop functioning. The main question is how can we take control and re-register the domain under our company's name?
Additionally, the company intends to move the website to a more reliable server. It's also important to note that the trademark is not registered under our ownership. How should we proceed in this complicated situation?

Firstly, regarding the domain name, you should quickly check the domain registration details using a WHOIS lookup to see if the domain is registered under your company's name or not. If it's not, you will need to take steps to re-register it in your company's name.

If the domain is not registered under your ownership, you can contact the current domain registrar to explain the situation and request a domain ownership transfer. You will likely need to provide documentation to prove your company's ownership and legitimacy. The registrar will guide you through the process, which may involve completing a domain transfer form and possibly paying a fee for the transfer.

Regarding the website and server migration, as a web designer, I recommend finding a reliable web hosting provider with excellent customer support and a strong track record of uptime and security. You can then work with the new web hosting provider to migrate the website to their servers. This may involve transferring the website files, databases, and configuring the DNS settings to point to the new server.
In parallel, it's crucial to address the trademark issue. I highly recommend consulting with a legal expert or intellectual property attorney to understand the implications of not owning the trademark associated with your website. They can advise you on the necessary steps to take to protect your company's intellectual property and ensure that you are not infringing on any existing trademarks.

You still have nearly a year before the domain expires. It's important to contact the registrar and request to pay for the domain by simply stating, "I want to pay for the domain for the administrator." Since you are in Podolsk, it might be more convenient to visit the registrar's office in person rather than sending a letter, as you can make the payment immediately.
Additionally, you should bring your documents to verify if any domain is registered to you. Remember not to publicly share your domain details. I hope to see the issue resolved within the year.

I'd say that if the domain is registered under someone in your organization, such as your boss or an employee, gaining control of it shouldn't be too challenging. The first step would be to determine the owner of the domain.

Have you received any notifications regarding the expiration of the registration period to any of the known email addresses? It might be worth trying to send a test message to these addresses. If you receive a response, there is a chance that you can contact the registrar through that email. Otherwise, you may need to visit the registrar's office in person.

If the domain's registration details do not belong to anyone in your organization, then your best bet would be to search for a skilled programmer who can assist with this matter.