Yes, and it's advisable to protect your brand. Domain names, often synonymous with business names like Amazon.com for Amazon.com Inc., can be trademarked. Registering your domain as a trademark safeguards it and prevents others from securing similar domain names. This process is akin to business name registration but at the domain level, with organizations like ICANN overseeing it. Ensure to register your trademark in the countries where your domain is registered, like your-domain-name.fr in France or your-domain-name.cn in China, to secure market-specific protection.