Hi @Nathan Keats ,
Are you using Exchange account? Email addresses are not shown for internal (Exchange) messages but do show for external addresses. As far as I know, there is currently no option available in the Outlook desktop client or from an Exchange or Office 365 admin perspective to change this display.
I have already submitted this feedback on the dedicated portal via the link below: https://feedbackportal.microsoft.com/feedback/idea/b53fae23-b5f8-ed11-a81c-000d3ae5b6f4
Many features of our current products are designed and upgraded based on customers’ feedback. With requirements like this increase, the problem may well be released in the future.
You can mark my reply as an answer, so that other users in the forum who have similar problems can also vote.
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