Given that "Kim" will be universally recognized as simply a shortened form of "Kimberly" by even the dimmest witted TSA drone or check in agent, I think it is highly unlikely you will have problems upon departing the US. At most, you'll get a "don't do that next time." You're slightly more likely to have issues on your return when dealing with agents who might not recognize the short name.

I've had clients book tickets in a shortened of my name before asking (Alex vs Alexander) and never had any real trouble, nor did I expend any effort trying to get it fixed. I was once asked internationally if "Alex" was really a shortened name, so I showed a credit card with it and that satisfied them.