@Jason Donnell thank you for this question.
The difference in the instance name reported in App and the telemetry in Application Insights seems to be related to way the web app is hosted in Linux based vs Windows based App Service. Linux apps in App Service run in their own containers. Therefore, it might be possible that the instance name reported by Azure App Service on Linux may be different from the current instance because the app may be running on a different container than the one it was previously running on.
In order to avoid such issues, I would suggest using ITelemetryInitializer
to override the default telemetry context's "Role Name" and "Role Instance". This would bring in uniformity in the application's instance name as reported by app and in the telemetry being sent to AppInsights. Please see this link for details - Set or override cloud role name.
Please let me know if you have any questions.