Question Summary:
Where did Imam Abū Hanīfah (rahimahu Allah) get the title Al-Imam Al-Azam?

Question Detail:

 
Where did Imam Abu Hanifa (RA) get the title Al-Imam Al-Azam?

Answer :

In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh. 
Hereunder are comments of great luminaries of Islam who have referred to Imam Abū Hanīfah (rahimahu Allah) with honorable titles, including Al Imām Al A‘zam:
1). Makkī ibn Ibrahim (d. ca 215 a.h.[1]) said[2],
كان أعلم أهل زمانه
He (Abū Hanīfah) was the most knowledgeable of his time
2). ‘Abdullah ibn Mubārak (d.181 a.h.[3]) composed a poem[4],
لقد زان البلاد ومن عليها - إمام المسلمين أبو حينفة...
Indeed the Imam of the Muslims, Abū Hanīfah, has beautified the lands and their inhabitants…
3). Imam Abu Al Hasan Al Ash‘arī (d. ca 330 a.h.[5]) says[6],
...وحاشى الإمام الأعظم أبو حنيفة رضي الله عنه من هذا القول
…And Al Imam Al A‘zam Abū Hanīfah is far from this accusation.
4). Imam Al Dabūsī (d.430[7]) discussing a principle says[8],
وعند الإمام الأعظم أبي حنيفة رحمه الله تدخل الأولى ولا تدخل الثانية
…And according to Al Imam Al A‘zam Abū Hanīfah (rahimahu Allah) the first applies and not the second.
5). Al Mawsilī (d.683[9]) mentions him in the foreword of Al Mukhtār[10],
فَقَدْ رَغِبَ إِلَيَّ مَنْ وَجَبَ جَوَابُهُ عَلَيَّ أَنْ أَجْمَعَ لَهُ مُخْتَصَرًا فِي الْفِقْهِ عَلَى مَذْهَبِ الْإِمَامِ الْأَعْظَمِ أَبِي حَنِيفَةَ النُّعْمَانِ
…So someone whose compliance is necessary upon me requested that I compile for him a brief book in fiqh based on the madh-hab of Al Imam Al A‘zam Abū Hanīfah
 
6). Imam Al Dhahabī (d.748[11]) in writing Imam Abū Hanīfah’s biography introduces him as[12],
أبو حنيفة الإمام الأعظم فقيه العراق النعمان بن ثابت
Abū Hanīfah, Al Imam Al A‘zam, the jurist of Iraq, Al Nu‘mān bin Thābit
 
 
7). Imam Al Safdī (d.764[13]) compiling those who have the title “Abū Hanīfah” says[14],
أَبُو حنيفَة جمَاعَة مِنْهُم الإِمَام الْأَعْظَم صَاحب الْمَذْهَب اسْمه النّعمان
Abū Hanīfah, there are many, from amongst them: Al Imam Al A‘zam, the one who has a madh-hab, his name is Nu‘mān
 
8). Imam Al Qurashī (d.775[15]) in writing Imam Abū Hanīfah’s biography introduces him as[16],
الإِمَام الْأَعْظَم أَبُو حنيفَة النُّعْمَان بن ثَابت
Al Imam Al A‘zam, Abū Hanīfah Nu‘mānbin Thābit
 
Reading the biography of Imam Abū Hanīfah clarifies any doubt one may have of his excellence in ‘ilm and ‘amal.
You may find detailed discussions on the life of Imam Abū Hanīfah here: http://darulmaarif.com/reader-abu-hanifah/
And Allah Ta’āla Knows Best
Hisham Dawood
Student, Darul Iftaa
Chicago, USA
Checked and Approved by,
Mufti Ebrahim Desai.
www.daruliftaa.net