Like Honor and Profit you get three identity cards. What do you do with the extra two? You only need one of each identity card right?

ALSO: how do you tell the difference between Corp Neutral cards and Runner Neutral cards? Just the way the layout is?

Backs of the cards have different art as well.

For your first question; whatever you feel like I sleeve mine back-to-back in clear sleeves, for when I accidentally shuffle the ID into my deck.

You can also tell the difference between the Corp and Runner neutral cards, because the types of cards are different (e.g., resource, event, etc. vs. asset, operation, etc.).

I frequently test unreleased cards by printing out spoiler images and putting them in sleeves; extra IDs make great backing cards.

it's really just a side effect of printing, as seen here:
https://lh6.googleusercontent.com/-PZWhUQ_-vDE/UqUuK7imLaI/AAAAAAAACTY/F1Uc2qwGPH4/w919-h689-no/IMG_20131208_203832.jpg

Although with the advent of Conquest signature squads and the Upstalk spoiler about what the new Jinteki identity was offering, maybe this will not be so much of the case in the future.

That said unlike Conquest unless we have to see singles (limit 1 per deck may count) that could mean 3 IDs albeit different, in one pack which could be a bit much.