Site Mailboxes should be available to be configured by default for primary domain instead of defaulting to the first domain alphabetically.
Currently, when a corporate with multiple domains activates a SharePoint Online site mailbox, the email address assigned belongs to the first domain alphabetically.
If ZCompany is a nationally known recognized brand and they purchase a small, unknown ACompany; then ZCompany attempts to create a site mailbox to collaborate with clients, it will be created at @Acompany.com.onmicrosoft.com - a brand unrecognizable to the customers of ZCompany.
At first we thought this was a problem, but after escalating through Premier Support, SharePoint Support, Office 365 Email Support, and our Technical Account Manager, we were assured by all parties that this is the correct behavior by design. We were told by each representative, fix agent, and engineer, that an enhancement to the Office 365 product would need to be made in order to user our primary company domain in the email address and not the first domain alphabetically.