This is my solution(inspired from the solution of andersschuller at https://stackoverflow.com/a/23705160/1325574)  for the problem. There maybe some corner cases(Classloading) where this implementation does not work, but for the most simple cases it works.
I have created a small performance test of this with my limited jmh knowledge: 
https://gist.github.com/picpromusic/4b19c718bec5a652731a65c7720ac5f8
The "Named"-results are measured for the implementation of the answer of @stuartmarks Naming(toString) Lambda-Expressions for Debugging purpose
# Run complete. Total time: 00:40:31
Benchmark                        Mode  Cnt          Score         Error  Units
MyBenchmark.testNamedPredicate  thrpt  200   45938970,625 ±  615390,483  ops/s
MyBenchmark.testPredicate       thrpt  200   23062083,641 ±  154933,675  ops/s
MyBenchmark.testPredicateReal   thrpt  200   48308347,165 ±  395810,356  ops/s
MyBenchmark.testToString        thrpt  200  138366708,182 ± 1177786,195  ops/s
MyBenchmark.testToStringNamed   thrpt  200  252872229,907 ± 8044289,516  ops/s
MyBenchmark.testToStringReal    thrpt  200    6670148,202 ±   40200,984  ops/s
As you can see it is roughly 2 times slower than using an unnamed lambda. So be carefull in setting -DnamedLambdasEnabled=true. Interessting for me is that it is surprisingly expensive to call toString on an Real-lambda. Maybe someone can explain that, or my jmh-test is stupid.
Here is the code:
/**
 * Helper Class to give lambda a name ("toString") for debugging purpose
 *
 */
public class LambdaNamer {
    private static Method TO_STRING;
    static {
        try {
            TO_STRING = Object.class.getMethod("toString");
        } catch (NoSuchMethodException | SecurityException e) {
            throw new RuntimeException("There is something rotten in state of denmark!");
        }
    }
    /**
     * Overrides toString "Method" for a given lambda.
     * 
     * @param name toString result of lambda
     * @param obj the lambda to encapsulate
     * @return the named lambda
     */
    public static <T> T nameIt(String name, T obj) {
        if (Boolean.getBoolean("namedLambdasEnabled")) {
            Class<T> clazz = (Class<T>) obj.getClass();
            Class<?>[] interfaces = clazz.getInterfaces();
            return (T) Proxy.newProxyInstance(//
                    obj.getClass().getClassLoader(),//
                    interfaces, //
                    (Object proxy, Method method, Object[] args) -> {
                        if (TO_STRING.equals(method)) {
                            return name;
                        } else {
                            return method.invoke(obj, args);
                        }
                    });
        } else {
            return obj;
        }
    }
}
Do you have other solutions? Maybe something that does not have performance implications?