Salam alaykum Many Sunnis claim that Imam Ali named his sons after their three caliphs out of love for them. And they provide one Hadith where it says his son was named after Uthman ibn Affan, and not Uthman ibn Mazoon as the Shia belief is. I need proof from both Sunni and Shia ahadith that this is not true and InshaAllah those are available, Thank you and may Allah bless you.

Wa alaykum salam

وذكر فيه (الثقفي في تاريخه)، عن هبيرة بن ميرم قال: كنا جلوسا عند علي عليه السلام، فدعا ابنه عثمان، فقال له: يا عثمان، ثم قال: إني لم أسمه باسم عثمان الشيخ الكافر، إنما سميته باسم عثمان بن مظعون. أبو الصلاح الحلبي، تقريب المعارف، ص ٢٩٤

Al-Thaqāfi (in his book of history) has narrated from: Hubarātah b. Mariam, he said: We were sitting with Ali (as) & Ali (as) had called for his son ‘Uthmān to come, he said to him:O Uthmān, he continued and said: I did not name him ‘Uthmān because of the Kāfir Shaykh ‘Uthmān, for I named him ‘Uthmān because of ‘Uthmān b. Math’un.

Abu Salah al-Halabi, Taqreeb al-Ma’ārif, Pg. 294