I have seen this post Get excel user and saw that there is no such possibility. I have done research and found only one way to get these details if logged in with Microsoft Graph, I was wondering if at this moment of time the Office.js api has been made to expose the user's details as such.
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While it is still in Preview, you may want to take a look at Enable SSO in an add-in. This will give you a Graph token, allowing you to quickly grab the user's profile information.

Marc LaFleur
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