I purchased Office 365 subscription recently, and wanted to bind my own domain, because wanted to use e-mail address like alias@some_custom_domain.com
If you want to use custom domains, manual page suggest to change name server records for your domain to ns1.bdm.microsoftonline.com and ns2.bdm.microsoftonline.com. After doing this you can use aliases with your domain for Exchange mail and Lync.
If you don’t want to change by any reasons name servers for your domain, just go through steps:
1) open Domains page in your admin
2) click on your custom domain my_custom_domain.com
3) on the domain page click DNS Dispatcher
4) you can see “system’s” Office 365 MX, CNAME, TXT and SRV records (screenshot in my native Russian lang, but I think it’s not a problem to understand):
Add this records to your domain, and wait some time (about 10-30 min). After that you can use your custom domain to create users with full access to Office 365 services, and without using MS name servers.
Warning! This method is NOT suitable for any enterprise customers!! Because if “system” records are changed, your users can’t use one or any services (Exchange, Lync, etc) until you manually fix your domain records.
I tried to do it, and it’s working. I use Office 365 privately, so I wake up to a risk.
Good luck! ;)