The opponents of Shia Muslims put this allegation on Imam Ali (AS) trying to justify their claim that Imam Ali (AS) was friendly with the three Caliphs of Saqeefah. Imam Ali (AS) never gave any of his children any name of his opponents. It is authentic that he gave the name Othman to one of his sons and clearly said: I am giving him the name of my brother Othman Ibn Madh'oon عثمان بن مظعون who was a pious follower of Imam Ali (AS) and passed away during the life of the Prophet Muhammad (SAWA) and he was the first companion who was burried in the Baqee'.
Imam Ali (AS) never gave the name of Abu Bakr nor Omar to any of his children. He gave the name of Amro عمرو which is written in Arabic like عمر but it was not Omar.
Many of our scholars say the these names where not confined to the three rulers of Saqeefah but usual names used by people in general.
The stand of Imam Ali (AS) from the three rulers of Saqeefa is very clear in manybtexts e.g. his sermon known as Al-Shaqshaqiyyah and what is narrated in Saheeh Muslim ( Volume 5, page 153 from Omar Ibn al-Khattab who said that Ali believed that Abu Bakr and Omar are liars, sinners, betrayers, and dishonest.