Yes — the federal Personal Data Protection Law applies to businesses of any size processing personal data in the UAE, and an online store holding names, addresses and order histories falls squarely within it. There is no small-business exemption. The obligations are practical rather than frightening: collect data only for clear purposes, have a lawful basis (usually the customer's consent or the order itself), explain what you collect and why in a privacy notice, keep the data secure, delete it when no longer needed, and respond when customers ask to access or erase their information. Appointing a dedicated data protection officer is only required in limited higher-risk situations that a small store will not normally meet. Start by mapping what data you hold and where it sits, publishing a plain-language privacy policy on your site, adding a separate consent tick-box for marketing emails, and checking that your payment and delivery partners handle data responsibly. Note that DIFC and ADGM run their own separate data protection regimes, so where you are licensed matters. A UAE lawyer familiar with data protection can confirm exactly which regime covers you and review your policies before a customer or regulator does.