Green idea in similar form to Vengeance of the Sun. Possibly would need to be bumped to rare though?

Is that trigger even possible? Increasing Discovery is not a distinctive event unlike gaining life or playing a land, so I'm not sure if this can work.

If that's the case, neither does Vengeance of the Sun work. I don't see how the trigger isn't possible though. Your Discovery = lands you control with diff names. A land with a diff name ETB = your discovery increases. Admitedly, I was unsure about the original wording on Vengeance of the Sun but DJK thought it worked. When I tried to think of alternative wordings things got convoluted, or at least it's more wordy and confusing to directly go "Whenever a land enters the battlefield under your control with a different name from another land you control".

We can pack into the Discovery rules a rule explaining the more that this wording translates fully to when a land enters the battlefield under your control with a unique name. That's just a conditional variation on the landfall trigger so it should work.

The biggest concern I have with this wording is if people will misunderstand how it works. I want to try it out because I think it should be an intuitive and appealing wording for most people.

Any good reason why this doesn't grant haste like with Awaken?

I just compared it to other "increase" triggers, and most of them are tied to a certain event that went over the stack, like "whenever you gain life" is tied to the effect "gain life", or "lose life" is tied to "life loss". Additional rules might fix that though, true.

I guess Haste simply didn't occur to me. The other card I came up that does this so far, Awaken Terrain, doesn't grant haste either. There's also the fact that it's green/blue.

Regarding the conditional trigger of Discovery, would that also count cards that become lands via transformation? If not, those cards probably need an "exile-->enter again" transformation like the sparkers or something.