The title of Hazrat Umar (ra) was Abu Hafs.
(Ibn Hajar al-Asqalani, Al-Isabah fi Tamyiz al-Sahabah, Vol. 4, Umar (ra) bin al-Khattab [Beirut, Lebanon: Dar al-Kutub al-Ilmiyyah, 2005], p. 484)
Hazrat Ibn Abbas (ra) relates that on the day of the Battle of Badr, the Holy Prophet (sa) said to his companions:
“I have heard that some of the members of the Banu Hashim and a few others have been forced against their will to come along with the Quraish and they do not wish to fight against us. Therefore, whosoever amongst you comes up against anyone from the Banu Hashim, he should not kill him. And whoever sees Abu Al-Bakhtari, should not kill him. And whoever sees Abbas bin Abdil Muttalib” who was the paternal uncle of the Holy Prophet (sa), “should not kill him. This is because all of these people have been forced to come with the Quraish.”
Hazrat Ibn Abbas (ra) relates that Hazrat Abu Huzayfara bin Utbah stated, “Are we to kill our fathers, sons, brothers and other relatives and let Abbas live. By God, if I find him”, i.e. Abbas, “I will kill him with my sword.”
The narrator states that when news of this reached the Holy Prophet (sa), he addressed Hazrat Umar (ra) bin Al-Khattab by saying “O Abu Hafs!” Hazrat Umar (ra) states, “I swear by Allah, this was the first time that the Holy Prophet (sa) addressed me with the title of ‘Abu Hafs’.”
The Holy Prophet (sa) then stated, “Will a sword be struck against the face of the uncle of the Messenger (sa) of Allah?” Hazrat Umar (ra) submitted, “O Messenger (sa) of Allah! Grant me permission to sever the head of the individual who has uttered these words. By Allah, he” i.e. Abu Huzayfa, “has displayed hypocrisy.” Hazrat Abu Huzayfara would later say, “Ever since I uttered those words on that day, I had never felt at ease and was always anxious owing to what I had said, and only martyrdom could serve as an atonement for this.” Thus, Hazrat Abu Huzayfara attained martyrdom in the Battle of Yamamah.
(Ibn Hisham, Sirat Ibn Hisham, Vol. 1, Bab Ghazwat Badr [Egypt: Mustafa al-Babi, 1955], p. 429)
Hazrat Aisha (ra) states that the Holy Prophet (sa) gave Hazrat Umar (ra) the title of Farooq.
(Ali Ibn al-Athir, Usd al-Ghabah fi Ma‘rifat al-Sahabah, Vol. 4, [Beirut, Lebanon: Dar al-Kutub al-Ilmiyyah, 2003], p. 143)
We find a narration regarding the context of this in which Hazrat Ibn Abbas (ra) relates:
“I enquired of Hazrat Umar (ra) as to how he was given the title of Farooq. He replied, ‘Hazrat Hamzah (ra) accepted Islam three days before I did. Coincidentally I headed to the Holy Mosque and Abu Jahl approached the Holy Prophet (sa), hurling abuse at him. Following this, he informed Hazrat Hamzah (ra) of what he had done.
“When Hazrat Hamzah (ra) came to know of this, he took his bow and headed towards the Ka‘bah. He stood in front of the gathering of the Quraish in which Abu Jahl was seated, leaning on his bow and glaring at Abu Jahl. Sensing displeasure from Hazrat Hamzah’s (ra) face, Abu Jahl said, ‘O Abu Ammarah!’ This was the title of Hazrat Hamzah (ra). ‘What is the matter?’ Hearing this, Hazrat Hamzah (ra) struck his bow on Abu Jahl’s face with such force that his cheek was cut and it started bleeding. Fearing his rage, the Quraish immediately put an end to the quarrel.” The narrator states that he did not personally witness what Hazrat Umar (ra) narrated about that day.
“Three days after this incident I went out and on the way, I met a person from the Banu Makhzum. I asked, ‘Have you forsaken the religion of your forefathers and adopted the religion of Muhammad (sa)?’ He replied, ‘What would it matter if I have done so? They too have done so over whom you have more right than myself.’ Hazrat Umar (ra) then asked, ‘Who do you speak of?’ He answered, ‘Your sister and brother-in-law.’ Hazrat Umar (ra) states, ‘Having heard this, I went to my sister’s house and found the door locked. I could hear some whispers from inside. The door was then opened for me and I entered. I then asked them, “What did I just hear you saying?” They replied, “What did you hear?” During the conversation, the matter escalated and I grabbed my brother-in-law by his head and struck him, causing him to bleed. My sister got up and held me by the head saying, “This happened against your wishes, i.e. our acceptance of Islam.”’”
In any case, in another narration there is mention of his sister also being injured. Hazrat Umar (ra) says, “When I saw the blood of my brother-in-law”, or it could have been that of his sister, “in that moment, I felt ashamed so I sat down and said, ‘Show me this parchment.’ My sister replied, ‘Only the pure can touch it. If you speak the truth, go and wash yourself.’ So I washed myself and came and sat down. They brought the parchment to me on which it was written:
بِسْمِ اللّٰهِ الرَّحْمٰنِ الرَّحِيْمِ
“[In the name of Allah, Most Gracious, Ever Merciful.] I said, ‘These names are very pure and virtuous.’ Then it was written:
طٰهٰ مَا اَنْزَلْنَا عَلَيْكَ الْقُرْاٰنَ لِتَشْقٰى
“[Ta Ha. We have not sent down the Quran to thee that thou shouldst be distressed] and he read up to:
لَهُ الْاَسْمَآءُ الْحُسْنٰى
“[(He is) Allah. There is no God but He. His are the most beautiful names.]” These were the verses 2-9 of Surah Ta Ha.
Hazrat Umar (ra) states:
“I developed a great degree of respect in my heart for these words. I then said, ‘The Quraish flee from this, but I have accepted Islam,’ and asked, ‘Where is the Holy Prophet (sa)?’ My sister answered, ‘He is in Dar al-Arqam.’ I reached there and knocked on the door. The companions gathered around. Hazrat Hamzah (ra) asked them, ‘What is the matter with you people?’ They replied, ‘Umar!’ Hazrat Hamzah (ra) then said, ‘Even if it is Umar, open the door for him if he is standing outside. If he has come with good intentions, we shall accept him. But if he has come with evil intentions we shall slay him.’”
The Holy Prophet (sa) also heard this. He went outside, then Hazrat Umar (ra) recited the declaration of faith, upon which all the companions present there exclaimed, “Allah is the Greatest” [Allahu Akbar], which was heard by all the people of Mecca. Hazrat Umar (ra) continues, “I then asked, ‘O Messenger (sa) of Allah, are we not on the truth?’ The Holy Prophet (sa) answered, ‘Indeed.’ I then asked, ‘Then why do we keep our religion hidden?’ Thereafter we formed two rows and set forth; I was in one of the rows and Hazrat Hamzah (ra) was in the other, until we reached Masjid Al-Haram and entered it. Thereupon, when the Quraish saw me and Hazrat Hamzah (ra) they were overcome with such grief and pain, the likes of which they had never felt before. Thus, on that day, the Holy Prophet (sa) gave me the name ‘Farooq’ because Islam was strengthened and truth and falsehood were distinguished from one another.”
(Jalaluddin Abd al-Rahman bin Abi Bakr al-Suyuti, Tarikh al-Khulafa, pp. 91-92, Lebanon, 1999)
Ayyub bin Musa relates:
“The Holy Prophet (sa) stated, ‘Undoubtedly Allah the Almighty has placed the truth in the words and heart of Hazrat Umar (ra) and he is the Farooq, for Allah the Almighty has distinguished between truth and falsehood through him.’”
(Ali Ibn al-Athir, Usd al-Ghabah fi Ma‘rifat al-Sahabah, Vol. 4, [Beirut, Lebanon: Dar al-Kutub al-Ilmiyyah, 2003], p. 143)