Use the Salesforce License Management App (LMA) to Track License Records for Package Installation in Sandbox

In order to differentiate the licenses for sandbox installations from those that are for production installations, you must add the custom checkbox field 'sandbox' on 'license' object to the license record page layout.

Packages installed in a sandbox default to a Site-based license.  The LMA manager can modify the license if they choose, but regardless of what the defaults are, it will always show as a Site-based license for sandbox installs.

Both Salesforce Classic and Lightning Experience support the LMA. For more information, please review Manage Licenses for Managed Packages.