Arduino: How to get the board type in code
Thanks to the help of Charlie Hanson and jantje I found the universal solution!

Because it is a pity that every Arduino programmer has to go through the same pain to figure out how to get the board name, I will offer my code to the public so everybody can just copy and paste it.

Here it is:

#if defined(TEENSYDUINO) 

    //  --------------- Teensy -----------------

    #if defined(__AVR_ATmega32U4__)
        #define BOARD "Teensy 2.0"
    #elif defined(__AVR_AT90USB1286__)       
        #define BOARD "Teensy++ 2.0"
    #elif defined(__MK20DX128__)       
        #define BOARD "Teensy 3.0"
    #elif defined(__MK20DX256__)       
        #define BOARD "Teensy 3.2" // and Teensy 3.1 (obsolete)
    #elif defined(__MKL26Z64__)       
        #define BOARD "Teensy LC"
    #elif defined(__MK64FX512__)
        #define BOARD "Teensy 3.5"
    #elif defined(__MK66FX1M0__)
        #define BOARD "Teensy 3.6"
    #else
       #error "Unknown board"
    #endif

#else // --------------- Arduino ------------------

    #if   defined(ARDUINO_AVR_ADK)       
        #define BOARD "Mega Adk"
    #elif defined(ARDUINO_AVR_BT)    // Bluetooth
        #define BOARD "Bt"
    #elif defined(ARDUINO_AVR_DUEMILANOVE)       
        #define BOARD "Duemilanove"
    #elif defined(ARDUINO_AVR_ESPLORA)       
        #define BOARD "Esplora"
    #elif defined(ARDUINO_AVR_ETHERNET)       
        #define BOARD "Ethernet"
    #elif defined(ARDUINO_AVR_FIO)       
        #define BOARD "Fio"
    #elif defined(ARDUINO_AVR_GEMMA)
        #define BOARD "Gemma"
    #elif defined(ARDUINO_AVR_LEONARDO)       
        #define BOARD "Leonardo"
    #elif defined(ARDUINO_AVR_LILYPAD)
        #define BOARD "Lilypad"
    #elif defined(ARDUINO_AVR_LILYPAD_USB)
        #define BOARD "Lilypad Usb"
    #elif defined(ARDUINO_AVR_MEGA)       
        #define BOARD "Mega"
    #elif defined(ARDUINO_AVR_MEGA2560)       
        #define BOARD "Mega 2560"
    #elif defined(ARDUINO_AVR_MICRO)       
        #define BOARD "Micro"
    #elif defined(ARDUINO_AVR_MINI)       
        #define BOARD "Mini"
    #elif defined(ARDUINO_AVR_NANO)       
        #define BOARD "Nano"
    #elif defined(ARDUINO_AVR_NG)       
        #define BOARD "NG"
    #elif defined(ARDUINO_AVR_PRO)       
        #define BOARD "Pro"
    #elif defined(ARDUINO_AVR_ROBOT_CONTROL)       
        #define BOARD "Robot Ctrl"
    #elif defined(ARDUINO_AVR_ROBOT_MOTOR)       
        #define BOARD "Robot Motor"
    #elif defined(ARDUINO_AVR_UNO)       
        #define BOARD "Uno"
    #elif defined(ARDUINO_AVR_YUN)       
        #define BOARD "Yun"

    // These boards must be installed separately:
    #elif defined(ARDUINO_SAM_DUE)       
        #define BOARD "Due"
    #elif defined(ARDUINO_SAMD_ZERO)       
        #define BOARD "Zero"
    #elif defined(ARDUINO_ARC32_TOOLS)       
        #define BOARD "101"
    #else
       #error "Unknown board"
    #endif

#endif


You can even put this code into a new header file and #include it into your project.

P.D.
If you want to know additionaly to the board also the CPU model, search for the file avr_cpunames.h