Nina - From Russian name Nina that comes from Slavonic ninati "nod", "doze" i.e. "dreamer". It spread due to Lermontov's "Mascarade" drama, which was staged in 1980s. It is in use now.
Aleksanyan - patronymic from the personal name Aleksan, a short form of Aleksander (see Alexander).
This form (transliteration) of the surname is found mainly in Armenia and Russia.