How does the WP repository determine that two plugins are the same when counting active installs?

Downloads and active installs are not the same thing:

  • downloading from .org does not increase the active download stats, those are separate
  • it’s the update check that’s used to calculate this

So no steps are necessary on your part other than keeping the plugin name/slug the same. Otherwise there are no options available to you for influencing the statistics outside of this. If you ask them to incorporate stats from additional sources that you are providing they will say no.