Not really an Eve main, but I play her a bit. Here's my 2 cents.
Make her identity a bit more concrete. Sure, she's an assassin, but like... what is she?
Master Yi is a master swordsman who taught Wukong the art of Wuju.
Heimerdinger is a yordle mechanic/inventor.
Garen is a demacian soldier who was born into the military.
Eve is... this blue chick that assassinates stuff?
Give her more burst. She has a bit more sustained damage and relies on allies until getting ahead. Kinda destroys the idea of an assassin.
Don't let her ult scale of current health. Assassins kill weaker things, not do less damage as they get weaker. Make things scale off of missing health as an execute.
The stealth mechanic is cool, but make it easier to balance. I'm not sure how to go about that... something to think about.
Her Q is cool, but it is more of a "I have to hit this whenever someone is close" rather than a tactical decision. Put more weight on it through a longer cooldown and more damage or the like to make it more interactive.
Her E is a bit... plain. Click to do damage. Maybe make it do more damage when attacking from behind, or make her Q apply a mark that it consumes, or maybe make it build charges while in stealth like a Statikk Shiv... idk.
Her W seems to be the one thing I think could be kept. It requires timing to get good use out of it, and it gives counterplay but forcing her to break stealth.
Back to her R, make it more of an execution making it more of a Siphon would be cool, so that it would have a tradeoff. Ult a squishy for more damage, or ult a tank for a bigger HP shield. I like the %HP scaling mechanic though, just make it more "assassin-y."