Prepared with base on research by TripolySunni.

Well, it was narrated in shia books, that Imam Abu Jafar said:

So you can see how Evil the names of the enemies of ahlul-bayt are that if you mention them even Iblis would shake from how evil they are.  If you ask any Shia today about the names of the enemies of Ahlu-bayt he’ll tell you: “Umar, Aisha, Abu bakr, Uthman ect…” Now here’s the thing, it seems Shia Imams like to “Shake the Devil” by naming their own children after their enemies.

-‘Aisha bint Musa al Kathim bin Ja’afar al Sadiq (rah):
She is from the daughters of Imam Musa and this was mentioned by many of the Shia scholars including Sheikh al Mufid in his “al-Irshad” page 303, “‘Umdat al-Talib” by ibn ‘Anbah in the margin of page 266.

Shia scholar Ni’imatullah al Jazaeri writes in his “al-Anwar al Nu’umaniyyah” 1/380: ” As for his children he has thirty seven sons and one daughter, from his sons are: Ali al-Reda and … and his daughter ‘Aisha”. at-Tustari has mentioned more from his daughters in the book “Tawarikh al-Nabi wal Aal” pages 125,126: “Fatima al-Kubra, Fatima al-Sughra, Ruqayyah, Ruqayyah al-Sughra, Hakima, Umm Abiha, umm Kulthoum, Umm Salamah, Umm Ja’afar, Lubanah, ‘Aliyyah, Aaminah, Hassanah, burayha, ‘Aisha, Zeinab and Khadeeja.”

-‘Aisha bint Ali al-Hadi bin Muhammad al-Jawad (rah):
In his “Ihqaq al-Haqq” 19/623, at-Tustari wrote: “He (Ali al-Hadi) had five children: Imam al-Hassan al-‘Askari, al-Hussein, Muhammad, Ja’far and ‘Aisha…”

Sheikh al-‘Amili in “A’ayyan al Shia” 2/36:
“Abu al-Hassan Ali al-Hadi ibn Muhammad al-Jawad… His children: he had the Imam after him Abu Muhammad al-Hassan and al-Hussein and Muhammad who died during the life of his father and Ja’afar who claimed Imamah after his brother’s death and was called the Liar and his Daughter ‘Aisha.”

Sheikh al-Tabari in “Dalael al-Imamah” page 410:
“Mentioning his children: Abu Muhamad al-Hassan the Imam PBUH, al-Hussein, Ja’afar and from the daughters ‘Aisha.”

And we all know how many shia imams called their children with names: Abu Bakr, Umar and Uthman!