Microsoft.ApplicationInsights.AspNet has been renamed to Microsoft.ApplicationInsights.AspNetCore

[dnduffy]

The SDK Microsoft.ApplicationInsights.AspNet has been renamed to Microsoft.ApplicationInsights.AspNetCore to align with the naming in ASP.NET Core itself.
This is a breaking change.
The old package supports ASP.NET RC1 whereas the new package is built against the latest release of ASP.NET RC2. Due to breaking changes between ASP.NET RC1 and RC2 the old ApplicationInsights package will no longer be updated and all future updates will be using the new name Microsoft.ApplicationInsights.AspNetCore.

We have updated the SDK to use the .NET Core CLI runtime environment which picks the latest set of RC2 dependencies. Please note that this version is not compatible with RC1 bits or the DNX environment.

In order to update to the latest ApplicationInsights SDK for ASP.NET please remove any references to the old NuGet package and install the new named package instead (references can be found in the project.json file).
See here for migration steps from ASP.NET RC1 to RC2: https://docs.asp.net/en/latest/migration/rc1-to-rc2.html#namespace-and-package-id-changes
We apologize for the inconvenience of a manual upgrade to a new package name. We chose not to create an automatic migration from the old to new package naming because this could inadvertently break customers still using DNX or other pre-RC2 ASP.NET technologies who are not ready to migrate to .NET Core CLI and ASP.NET RC2.