Yes, it is possible to create a website with two different businesses, such as graphic and UI/UX design services and an e-commerce store, using your own domain name instead of an Odoo subdomain. Odoo allows you to set up and manage multiple websites from a single database. Here’s how you can do it:

1. Set Up Your Domain: Purchase a domain name and configure it to point to your Odoo server.
2. Create Multiple Websites: In Odoo, navigate to the Website app and create multiple websites, one for each business.
3. Customize Each Website: Use Odoo’s website builder to customize each site according to its business focus, including design, content, and e-commerce functionalities.
4. Manage from One Backend: Use Odoo’s integrated backend to manage both websites, including products, services, orders, and customer interactions.

This setup allows you to have a unified management system while maintaining distinct online presences for each business.

https://www.odoo.com/documentation/saas-17.2/applications/websites/website/configuration/domain_names.html?highlight=domain