Haneef is the one who is true in his belief. It also refers to those people who during the time of jaahiliyyah (before Islam) rejected the idolatry in their society. These people were in search for the true religion of Prophet Abraham (Peace be upon Him). 
حَنِيف اسم : aright - correctly; rightly
حَنِيف: Unorthodox - not orthodox
حَنِيف : قَوِيم
Orthodox: TRUE - حَنِيف : قَوِيمُ الرَّأْ
Orthodox - holding correct or currently accepted opinions, especially on religious doctrine, morals, etc, or not independent-minded
حَنِيف : مُعْتَدِل
- without fault; free from defect or error
- well adapted or suited, good enough
- perfect, unblemished
- mild; kind; careful; not rough, violent or severe
- conforming to a standard; regular, usual, typical
- ready to use or listen to reason; sensible
- having proper or honest opinions, based on what is right
- self-restrained; self-controlled; moderate.
- intact; unimpaired; unharmed
- intact; unimpaired 
1. They say, "Be Jews or Christians [so] you will be guided." Say, "Rather, [we follow] the religion of Abraham, inclining toward truth, and he was not of the polytheists." Surah Al Baqarah 2:135
2. Abraham was neither a Jew nor a Christian, but he was one inclining toward truth, a Muslim [submitting to Allah]. And he was not of the polytheists. Surah Aal Imran 3:67
3. Say, "Allah has told the truth. So follow the religion of Abraham, inclining toward truth; and he was not of the polytheists." Surah Aal Imran 3:95
4. And who is better in religion than one who submits himself to Allah while being a doer of good and follows the religion of Abraham, inclining toward truth? And Allah took Abraham as an intimate friend. Surah Al Nisa 4:125
5. Indeed, I have turned my face toward He who created the heavens and the earth, inclining toward truth, and I am not of those who associate others with Allah." Surah Al An’aam 6:79
6. Say, "Indeed, my Lord has guided me to a straight path - a correct religion - the way of Abraham, inclining toward truth. And he was not among those who associated others with Allah."Surah Al An’aam 6:161
7. And [commanded], 'Direct your face toward the religion, inclining to truth, and never be of those who associate others with Allah. Surah Yunus 10:105
8. Indeed, Abraham was a [comprehensive] leader, devoutly obedient to Allah, inclining toward truth, and he was not of those who associate others with Allah. Surah Nahl 16:120
9. Then We revealed to you, [O Muhammad], to follow the religion of Abraham, inclining toward truth; and he was not of those who associate with Allah. Surah Nahl 16: 123
10. So direct your face toward the religion, inclining to truth. [Adhere to] the fitrah of Allah upon which He has created [all] people. No change should there be in the creation of Allah. That is the correct religion, but most of the people do not know. Surah Al Rum 30:30
1. Ibn 'Abbas (R) said, "The Prophet, ﷺ, was asked, 'Which religion does Allah Almighty love the most?' He replied, 'The simple Hanifiyya one.' Adab Al Mufrad Book 14, Hadith 287
2. Narrated Ibn 'Umar(R): Zaid bin 'Amr bin Nufail went to Sham, inquiring about a true religion to follow.
He met a Jewish religious scholar and asked him about their religion. He said, "I intend to embrace your religion, so tell me something about it." The Jew said, "You will not embrace our religion unless you receive your share of Allah's Anger." Zaid said, "'I do not run except from Allah's Anger, and I will never bear a bit of it if I have the power to avoid it. Can you tell me of some other religion?" He said, "I do not know any other religion except the Hanif." Zaid enquired, "What is Hanif?" He said, "Hanif is the religion of (the prophet) Abraham who was neither a Jew nor a Christian, and he used to worship None but Allah (Alone)"
Then Zaid went out and met a Christian religious scholar and told him the same as before. The Christian said, "You will not embrace our religion unless you get a share of Allah's Curse." Zaid replied, "I do not run except from Allah's Curse, and I will never bear any of Allah's Curse and His Anger if I have the power to avoid them. Will you tell me of some other religion?" He replied, "I do not know any other religion except Hanif." Zaid enquired, "What is Hanif?" He replied, Hanif is the religion of (the prophet) Abraham who was neither a Jew nor a Christian and he used to worship None but Allah (Alone)"
When Zaid heard their Statement about (the religion of) Abraham, he left that place, and when he came out, he raised both his hands and said, "O Allah! I make You my Witness that I am on the religion of Abraham." Sahih al-Bukhari 3827
One day when the Quraysh had assembled on a feast day to venerate and circumambulate the idol to which they offered sacrifices, this being a feast which they held annually, four men drew apart secretly and agreed to keep their counsel in the bonds of friendship. They were
(i) Waraqa b. Naufal
(ii) `Ubaydullah b. Jahsh
(iii) `Uthman b. al-Huwayrith
(iv) Zayd b. `Amr b. Nufayl b. b. diyy b. Ka`b b. Lu'ayy.
They were of the opinion that their people had corrupted the religion of their father Abraham, and that the stone they went round was of no account; it could neither hear, nor see, nor hurt, nor help. `Find for yourselves a religion,' they said; `for by Allah you have none.' So they went their several ways in the lands, seeking the Hanifiya, the religion of Abraham.
Waraqa attached himself to Christianity and studied its scriptures until he had thoroughly mastered them.
`Ubaydullah went on searching until Islam came; then he migrated with the Muslims to Abyssinia taking with him his wife who was a Muslim, Umm Habiba, daughter of Abu Sufyan. When he arrived there he adoped Christianity, parted from Islam, and died a Christian in Abyssina.
After his death the prophet ﷺmarried his widow Umm Habiba.
`Uthman b. al-Huwayrith went to the Byzantine emperor and became a Christian. He was given high office here.
Zayd b. `Amr stayed as he was: he accepted neither Judaism nor Christianity. He abandoned the religion of his people and abstained from idols, animals that had died, blood, and things offered to idols(The influence of the Jewish formula, taken over by early Christianity (Acts 15.29) is clear.). He forbade the killing of infant daughters, saying that he worshipped the Allah of Abraham, and he publicly rebuked his people for their practices.
Asma' d. Abu Bakr said that she saw Zayd as a very old man leaning his back on the Ka`ba and saying, `O Quraysh, By Him in whose hand is the soul of Zayd, not of you follows the religion of Abraham but I.' Then he said one: `O Allah, if I knew how you wished to be worshipped
I would so worship you; but I do not know.' Then he prostrated himself on the palms of his hands.
I was told that his son, Sa`id b. Zayd (R), and `Umar b. al-Khattab (R) , who was his nephew, said to the apostle, `Should we to ask Allah's pardon for Zayd b. `Amr?' He replied, `Yes, for he will be raised for the dead as the sole representative of a whole people.'