Hello Andrew Krimmel
Good day and thanks for posting in Microsoft community.
To achieve your goal of using "Send on Behalf" permissions without displaying the sender's email address in the recipient's view, you will need to understand the limitations of Outlook and Exchange when it comes to email headers.
When you send an email using "Send on Behalf" permissions, the default format for the sender's information is: From: John Doe <john*@domain.com> on behalf of Accounting <*@domain.com>. This includes both the sender's name and email address along with the shared mailbox name. Please note as for now, there is no built-in feature in Outlook or Exchange that allows you to completely hide the sender's email address while still using "Send on Behalf" permissions.
As it is related to Outlook product design, it is strongly recommended to submit your valuable feedback directly to the Microsoft product development team by either going to Help from your Outlook App > submit Feedbackor by posting on Outlook · Community (microsoft.com) for feature requests.
Please note that nobody here is the product developer or decision maker and has no control over the product. Everyone, including us as a community moderator, can only assist you with the query for providing available solutions and the feature's availability status within our scope and capability.
Your feedback is crucial in helping us understand user needs and preferences, and it can influence future updates and features.
Thank you for your time and understanding.
Sincerely,
Bertrand