Hello
Thank you for your question and reaching out. I can understand you are having query\issues related to Custom Domain.
Please make sure you have updated your DNS , MX and NS records for your custom domain so that It can talk your Office 365 subscription. and also make sure for Users Primary SMTP is updated as per your Custom domain email address.
In the Microsoft 365 admin center, choose Setup.
Under Get your custom domain set up, select View > Manage > Add domain.
Enter the new domain name that you want to add, and then select Next.
Sign in to your domain registrar, and then select Next.
Choose the services for your new domain.
Select Next > Authorize > Next, and then Finish. Your new domain has been added.
Also Azure AD Free plan should be sufficient in your case.
Reference :
https://learn.microsoft.com/en-us/microsoft-365/admin/setup/add-domain?view=o365-worldwide
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