Dear Jay Rennemeyer,
Good day! Thank you for posting to Microsoft Community. We are happy to help you.
We've went through your post carefully and under understand your concern that the Graph API not returning the name/URL info for the specific site in the JSON for a handful of users even though it returns every other site the user has access to, but since it’s related to Graph API and SharePoint integration with third-party Suitelet, we would like to suggest you to post your concern in the related Microsoft Community i.e., Microsoft Graph - Microsoft Q&A with SharePoint tag, SharePoint development tag and Graph tag to get the detailed help from the experts.
Apologies for redirecting you to different community as the members in the category posted focus on the users with the SharePoint Online out of the box concerns and have limited knowledge on the Graph API, so to get the fast and better assistance, we have redirected you in the correct guidance.
If the understanding above is not consistent with yours, please feel free to post back and point that.
Sorry for the inconvenience again. Your patience and understanding are highly appreciated. Hope you stay safe and healthy.
Sincerely,
Rhoda | Microsoft Community Moderator