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Thank you for choosing the Microsoft Online Community to bring your question.
To answer your question, yes, you can still get that custom domain name to work with your external website.
You sim0ply need to follow the instructions for setting up a site with a custom domain name.
If this does not resolve your issue, do not hesitate to respond and let me know. We can continue to research the issue until you get a suitable answer to your question.
Thank you again for choosing to use the Microsoft Online Community to bring your questions.
I understand that you are moving Office Live Small Business (OLSB) website to Office 365 website. Before moving on, I would like to confirm the current situation first.
1. Have you transferred the contents of the OLSB website to Office 365 website?
2. Have you added custom domains at the OLSB account? If so, did you buy it through OLSB directly?
3. If you have bought custom domains before, do you want to use custom domain with Office 365 services, such as public-facing website?
If you have bought custom domains from OLSB, please refer to the following video to move the custom domain to Office 365 and use the custom domain name as the public-facing website address.
In addition, could you please provide some screen shots of the issue occurred and a detailed example of the requirement. For tips, please click Use rich formatting > Insert image to upload the screen shots in the post manually.
How are the things going?
In addition, do you need further assistance on the issue?