Name in From address on emails

I have been submitting all tickets to our RT install by email using the mail gateway. Even when we take ticket submissions from our web site, we send them as an email from the requestor’s address. Then the generated emails to the AdminCC users have the requestor’s name in them, like

From: "<Requestor's name> from My Company" <myqueue@mycompany.com>

I have just started to submit tickets through the REST API instead (primarily so I can set some custom fields). The requestor is being set correctly but the email From address has the name of the RT user account I’m using for the REST API, rather than the requestor, like:

From: "Web RT Account from My Company" <myqueue@mycompany.com>

Is there a way I can fix this? I don’t see anything in the Scrip or Template settings.