Email Aliases are not used to logon, the UserPrincipalName is. Typically those match the PrimarySMTPAddress.
So if your Primary SMTP Address is user@Company portal .com and your user principal name is user@Company portal .com, then you logon as that.
If however you also have an email alias of OtherUser@Company portal .com, it will receive email sent to the alias, but you can not logon as OtherUser@Company portal .com to Azure/365 etc...
So, bottom line, what you are asking already exists.
Note also that Office 365 also support plus addressing now. Consider having your users sign up using aliases like those instead