Sending e-mail from an alias with corresponding display name

Some of our co-workers need to send mail from an alias that is not our default domain (but from a domain that is a sister company). I've got it set up, it works. When composing an e-mail users can select their 'from' address and select the alias from the sister company. The e-mail will be sent and the recipient can see the address with the chosen domain. The only thing is that the users display name will always be the one from the primary domain. We've got it set up like this:

Primary: Firstname Lastname | Company A
Alias: Firstname Lastname | Company B

When selecting the alias, I would like it if the display name could also be selected to come from Company B. Is there a fix or workaround for this issue? Seems like a waste of money to create a completely new second account for these users.