Add a new property ApplicationInsightsServiceOptions.EnableAuthenticatedUserTracking that adds the following to the emitted JS:

appInsights.setAuthenticatedUserContext("username".replace(/[,;=| ]+/g, "_"));

Note that it has to essentially be as if the user had done the following in the Razor view (this is from the AppInsights docs):

@if (User.Identity.IsAuthenticated)
{
    <script>
        appInsights.setAuthenticatedUserContext("@User.Identity.Name.Replace("\\", "\\\\")".replace(/[,;=| ]+/g, "_"));
    </script>
}