This situation occurs when a Microsoft Outlook user (the primary user) has permissions to Send As another Outlook user (the secondary user). The primary user will need appropriate permissions to be set in Microsoft Exchange to be able to do this. The permissions are Send As and, optionally, Full Control.

When Encryption Desktop PGP Tray is running, a message sent by the primary user but from the secondary user will appear in the Sent Items folder as sent by the primary user "on behalf of" the secondary user.

When PGP Tray is not running, a message sent by the primary user but from the secondary user will appear in the Sent Items folder as sent by the secondary user.

This is by design.

The contents of the From field in the message in the sender's Sent Items folder is cosmetic and does not affect functionality. 

Whether or not PGP Tray is running when the message is sent, the recipient of the message still sees the sender of the message as the secondary user.