Before you can use Lync, SharePoint Online and Exchange Online with a custom domain you need to add your custom domain to Office365. Follow these steps to complete setup of Exchange Online.
1. "Edit domain intent" of the domain to include "Exchange Online"
2. Get the DNS settings and add the records to your DNS these will look something like this:-
The @ that is in the Host name and the TXT Name didn't work for me, I left this blank and it worked well.
My settings look like this:
One hour is express in seconds I think but it didn't make any difference.
3. Create a user with the new domain – you can select the domain when creating the user.
4. Assign an exchange license to the user.
5. That's it – your new user should now be joe.bloggs@customdomain.com for example. Login as this user and send a few test emails before setting everyone else up.
