Can Energy Drinks Have A Negative Effects On Your Kidneys?

Yes.

The suspect ingredients in many energy drinks that are not so good for the kidneys include caffeine, sugar and phosphorous.  

Phosphorous is more of a risk in fizzy (carbonated) soda drinks, but some energy drinks have a fair dose of it, too.  The problem is that it promotes kidney stones.  There is a big increase in children being seen for kidney stone problems, and consumption of fizzy and energy drinks appears to be a factor.

Caffeine increases urine production, and effectively increases the body's demand for water.  This is a problem, because kidneys function best when they have more rather than less water in the system (the kidneys' job is to filter water-soluble waste out of the body).  So anything dehydrating the body makes more work and potentially stress for the kidneys, which could accumulate and lead to long-term damage.  Caffeine also interferes with the kidney's function of reabsorbing calcium; effectively, this promotes kidney stones, too.

Sugar.  High blood sugar levels (potentially just after someone has just had a high sugar meal) stimulates the kidneys to work extra hard in filtering the blood.  This extra load can cause cumulative damage, although in the main, only diabetics are normally at risk of such long-term damage.

There are other common ingredients in energy drinks that give cause for concern, especially sodium-based preservatives.

Yes energy drinks can negatively impact both kidneys and liver.
Don't drink them excessively.