The function of a white label in Astra is to just remove the Astra branding from the dashboard, and it does not change any code.
If we remove the mentions of Astra from the code, even WordPress will not understand that Astra theme is being used and so it will not detect any updates we release in future.
However, there are some plugins that take a different approach and can help you white label WordPress itself completely. Hide My WP Ghost plugin is an example of this. If you need to white label your website completely, you can consider similar plugins.