The name عَبْدُ اللَّهِ contains two syntactic elements:
عَبْدُ: muḍāf; it changes to nominative, accusative, or genitive according to its function.
اللَّهِ: muḍāf ilayh; it remains genitive.
The book calls the compound fully declinable because ordinary iḍāfa is not the mazjī-compound cause of diptote status.