onmicrosoft.com alias

Allinilla 

here is the details document that explains about OnMicrosoft cases you can and you cannot do.

If you want to have your email look like alan@contoso.com: buy the domain or just follow the steps in Add your users and domain to Office 365 if you own it already.

• You can't rename the onmicrosoft domain after sign-up. For example, if the initial domain you chose was fourthcoffee.onmicrosoft.com, you can't change it to be fabrikam.onmicrosoft.com. To use a different onmicrosoft.com domain, you'd have to start a new subscription with Office 365.

• You can't rename your team site URL. Your team site URL is based on your onmicrosoft.com domain name. Unfortunately, because of the way SharePoint Online architecture works, you can't rename the team site.

• You can't remove your onmicrosoft 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.

You can keep using the initial onmicrosoft.com domain even after you add your domain. It still works for email and other services, so it's your choice.