Technically this will work...
String name = new Object(){}.getClass().getEnclosingMethod().getName();
However, a new anonymous inner class will be created during compile time (e.g. YourClass$1.class). So this will create a .class file for each method that deploys this trick. Additionally, an otherwise unused object instance is created on each invocation during runtime. So this may be an acceptable debug trick, but it does come with significant overhead.
An advantage of this trick is that getEnclosingMethod() returns java.lang.reflect.Method which can be used to retrieve all other information of the method including annotations and parameter names. This makes it possible to distinguish between specific methods with the same name (method overload).
Note that according to the JavaDoc of getEnclosingMethod() this trick should not throw a SecurityException as inner classes should be loaded using the same class loader. So there is no need to check the access conditions even if a security manager is present.
Please be aware: It is required to use getEnclosingConstructor() for constructors. During blocks outside of (named) methods, getEnclosingMethod() returns null.