const MyClass = class Me {
  getClassName() {
    return Me.name;
  }
};

获取函数名

Object.getOwnPropertyNames(api.prototype)[1];

获取函数和类名

/**
 * Gets the classname of an object or function if it can.  Otherwise returns the provided default.
 *
 * Getting the name of a function is not a standard feature, so while this will work in many
 * cases, it should not be relied upon except for informational messages (e.g. logging and Error
 * messages).
 *
 * @private
 */
function className(object, defaultName) {
    var nameFromToStringRegex = /^function\s?([^\s(]*)/;
    var result = "";
    if (typeof object === 'function') {
        result = object.name || object.toString().match(nameFromToStringRegex)[1];
    } else if (typeof object.constructor === 'function') {
        result = className(object.constructor, defaultName);
    }
    return result || defaultName;
}

扩展阅读