Hello Ben,
Thanks for posting in the Apple Support Communities. We're happy to look into this with you. We understand that you're wanting to have different settings for profiles on an Apple TV device. Looking over the link below, it doesn't appear there is an option related to network settings for each profile.
Share Apple TV with multiple users - Apple Support
When each member in a household has an Apple ID, switching member profiles on Apple TV creates a custom experience, with Up Next lists, music, Game Center data, and content recommendations personalized for the currently active user.
If you'd like to see additional features or settings for each profile, you might submit feedback to Apple, for review. You can do so at Product Feedback - Apple.
Best regards.