Office 365 operated by 21Vianet creates a domain for you, like contoso.partner.onmschina.cn, when you sign up with the service. The user ID that you create when you sign up includes the domain, something like firstname.lastname@example.org.
Typically people use the initial domain while they’re using a trial version, to try out the services or while they're getting things set up. You can continue to use the partner.onmschina.cn domain as long as you like; it'll still work for email and other services, even if you add a custom domain. But most people add their own domain, like fourthcoffee.com, to Office 365 before they start using Office 365 for their organization so they can use a friendly, memorable email address and user ID with the service.
You may have two initial domains: partner.onmschina.cn and -public.sharepoint.cn
If you have a SharePoint Online Public Website, your Office 365 subscription may actually have two initial domains: the partner.onmschina.cn domain, that you chose when you signed up, and a SharePoint Online domain for your Public Website, created automatically for you.
You can use your partner.onmschina.cn domain (like fourthcoffee.partner.onmschina.cn) with most Office 365 services except with your public website. For example, you can use the partner.onmschina.cn domain with Office 365 email addresses (they are also your user IDs for Office 365), team sites, and Lync.
If you have a SharePoint Online Public Website (no longer available with new subscriptions), it's hosted on your initial SharePoint Online domain, like fourthcoffee-public.sharepoint.cn.
Note: Many organizations already have a website outside Office 365 that uses their custom domain name. If this is true for you, you don't need to think about or use the public-sharepoint.cn domain.
Renaming or removing the partner.onmschina.cn domain
There are some limitations about the initial partner.onmschina.cn domain.
You can’t rename your initial domain after sign-up. For example, if the initial domain you chose when you signed up for Office 365 was fourthcoffee.partner.onmschina.cn, you can’t change it to be fabrikam.partner.onmschina.cn. To use a different partner.onmschina.cn domain, you’d have to start a new subscription with Office 365.
You can't remove your initial domain.Office 365 needs to keep it around because it's used behind the scenes for your subscription. But you don’t have to use the domain yourself after you’ve added a custom domain.
However, if you like, you can keep using the initial partner.onmschina.cn domain even after you add your domain. It still works for email and other services, so it's your choice.