What are the full names of Abu Bakr Al-Siddiq and Abu Hurayrah (may Allah be pleased with them), and why was Umar named Al-Farooq? Is it because he differentiated between truth and falsehood?

There is disagreement regarding Abu Hurairah's name in the pre-Islamic era and in Islam. The most famous opinion is that his name was 'Abd al-Rahman ibn Sakhr, and the Prophet, may Allah's prayers and peace be upon him, gave him the kunya (agnomen) of Abu Hurairah. 'Umar was named al-Faruq because he distinguished between truth and falsehood. It is said that the first to name him so was the Prophet, may Allah's prayers and peace be upon him, and it is also said that the People of the Book named him thus, or that Gabriel, peace be upon him, named him so.