It is possible to get a free domain for your website, but usually these free domains have certain restrictions and limited selection:
Many hosting providers provide free 3rd or 4th level subdomains. Subdomains are the part of a domain name that comes before the main domain. For example, samename.domen.com. These subdomains can be useful for smaller projects, but may have limitations in terms of professional appearance and branding.
Some hosting providers offer free domains as part of their china email list packages. They may provide a free domain for the first year or longer, as long as you remain a customer.
Sometimes domain registrars and hosting providers offer free domains as part of promotions and special offers. These offers may change over time and their availability may vary by registrar or provider.
Some domain registrars offer free domains for educational and non-profit organizations. This may be a good option if your site meets these criteria.
Keep in mind that free domains may have limitations, such as lack of full control over domain records, the need to agree to the terms of free domains, and limited transfer options. If you have serious plans for your web project and want full control and a professional impression, consider registering a paid 2nd level domain through a domain registrar.