My Brilliant Friend title explanation

I think that "Brilliant" is how they both view each other, and that who is the "brilliant friend" shifts back and forth throughout their friendship. There's a certain edge of envy in their friendship. In the beginning, Lila is seen to be a prodigy, and Elena at one point says:

" When Lila stopped misbehaving and effortlessly outdid me, the teacher praised me first, with moderation, and then went on to exalt her prowess. I felt the poison of defeat more acutely when it was Sarratore or Peluso who did better than me ... Certainly I trained myself to accept readily Lila’s superiority in everything, and even her oppressions”(p32).

Then, Elena is able to continue on her education and Lila is not - Lila is jealous that Elena can continue down the path that she thought would be her way out of the neighborhood. While Elena moves into (and struggles in) the world of academia, Lila works in a factory and remains entrenched in the poverty of their childhood. Elena continues to find success as a writer and becomes known as 'brilliant' in her own right, but is still heavily affected by criticism she receives by Lila, who Elena continues to view as being the 'brilliant' one.

The dynamic between them is heavily influenced by these cycles of jealousy. I think that the phrase 'my brilliant friend' holds both bitterness and idolization of the other, summarizing their consistent rivalry throughout their lives. It implies a sense of resentment over the other's achievements, while also defining them by their relationship to the speaker.