الْحُسَيْنُ بْنُ مُحَمَّدٍ عَنْ مُعَلَّى بْنِ مُحَمَّدٍ عَنِ الْوَشَّاءِ عَنْ أَحْمَدَ بْنِ عُمَرَ قَالَ سَأَلْتُ أَبَا الْحَسَنِ (عَلَيْهِ السَّلام) لِمَ سُمِّيَ أَمِيرَ الْمُؤْمِنِينَ (عَلَيْهِ السَّلام) قَالَ لانَّهُ يَمِيرُهُمْ الْعِلْمَ أَ مَا سَمِعْتَ فِي كِتَابِ الله وَنَمِيرُ أَهْلَنا.

وَفِي رِوَايَةٍ أُخْرَى قَالَ لانَّ مِيرَةَ الْمُؤْمِنِينَ مِنْ عِنْدِهِ يَمِيرُهُمُ الْعِلْمَ

Narrated that Abu al-Hasan Imam Musa al-Kazim (عليه السلام) was asked,

"Why was Imam Ali (عليه السلام) named Amir al-Momineen (عليه السلام)?

Imam Kazim (عليه السلام) said, "Because He provided (Mayr) knowledge (ilm). Have you not heard in the book of Allah, "And we will get provision/food (Mayr) for our family." (12:65)

And in another narration it is said, "The reason being that the provisions of the believers is from Imam Ali (عليه السلام), He provided them knowledge"

[Source: al-Kafi, Vol. 1, Pg. 412]

Note: In the above hadith, Imam Kazim (عليه السلام) has derived the meaning from the root word "مير - Mayr" which means "to provide"