This book explores conflicting traditions (in this case the tradition of Judaism and the tradition of art), father versus son, contentedness with one's life versus peace in the family (the Jewish value of "shalom bayit"), the traditional Jewish world versus secular America.
My Name Is Asher Lev explores the nature of suffering. The discrimination that Asher’s father has against Asher's artistic tendencies can be related to the suffering of the many Jews in Russia and Germany that were oppressed by the government. Just as they were oppressed and punished for their beliefs, Asher is negatively viewed by his Father, his teachers, and his peers. Art is Asher’s real religion, and not only he, but his mother suffers for it. When Asher tries to portray his mother’s suffering, “his search for a motif reveals none powerful enough in his own tradition, and so he turns to the central theme of suffering in the Christian tradition: crucifixion.” 
Asher Lev's pursuit of art is complicated by his upbringing and training to see Jewish perspectives on beauty. Via his training, Asher Lev explores aesthetic traditions of beauty.
The book title itself signals Asher's issue with self-identity. Jacob Kahn tells Asher, "As an artist you are responsible to no one and to nothing, except to yourself and to the truth as you see it.”