The name Parthasarathy means 'charioteer of Partha' (another name for Arjuna). Krishna served as Arjuna's charioteer during the Kurukshetra war, delivering the Bhagavad Gita. Yudhishtara, Nakul, and Drishtadyumna were all Pandavas or allies but Krishna drove specifically for Arjuna (Phalguna).