Praise be to Allaah.
The thirty juz' of the Holy Qur'aan do not have special names by which they are known. This is indicated by two important matters:
The division of the Qur'aan into thirty juz' and sixty hizb - as is well known in the Mushafs that are widely available nowadays - is not something that was narrated from the Prophet (blessings and peace of Allah be upon him) and his Companions. Rather it is something worked out by al-Hajjaaj ibn Yoosuf al-Thaqafi (d. 110 AH), as it says in the history books, and it was implemented in the Mushafs, as he was in power at the time, and it has abided until the present day. It is a matter that some may have many reservations about, but it has to do with a minor matter and does not have to do with worship or beliefs. We have previously discussed this point in detail on our website, in the answer to question no. 109885.
The Standing Committee for Issuing Fatwas stated:
We do not know of any textual evidence for the system of division that appears in the margins of the Mushafs that people have in their hands nowadays. End quote.
Abd al-Azeez ibn Baaz, Abd al-Razzaaq Afeefi, Abd-Allah ibn Ghadyaan, Abd-Allah ibn Qaood
Fataawa al-Lajnah, 4/30
There is no report from the Sahaabah or from the Taabieen of special names for the thirty juz' of the Holy Qur'aan. Indeed we have not found that in the books on the sciences of the Qur'aan. Rather the names that are well known nowadays for some juz' are something that has been invented by those who memorised the Holy Qur'aan and by seekers of Qur'aanic knowledge, as a kind of shorthand and to make things easier. They are not names that have been narrated in reports. These names are: Juz' Amma, Juz' Tabaarak, Juz' Qad Samia, Juz' al-Dhaariyaat and Juz' al-Ahqaaf; beyond that, the other juz' are not known by special names because the juz' often begins in the middle of a soorah and not at the beginning.
To sum up, there are no special names for the juz' of the Holy Qur'aan that have been narrated in reports by the scholars.
And Allah knows best.