भरतर्षभः = भरतः ऋषभः इव – उपमितसमासः (कर्मधारयः) – Best among the lineage of King Bharata (भरत)
पुरुषर्षभः = पुरुष: ऋषभः इव – उपमितसमासः (कर्मधारयः) – Best among the men
कुरुणामृषभ: – कुरुणाम् ऋषभः – Best among Kuru lineage
ऋषभः means best or most excellent
Reference in the Scriptures
It is mentioned in Bhagavata Gita Chapter 3 verse 41
तस्मात्त्वमिन्द्रियाण्यादौ नियम्य भरतर्षभ।
पाप्मानं प्रजहि ह्येनं ज्ञानविज्ञाननाशनम्।।3.41।।
O Arjuana, best among in the lineage of Bharata ! With the help of controlled senses, you should kill this desires which is a destroyer of Knowledge and Science.
It is mentioned in Ramayana, Ayodhyakanda 49.14
सूत इत्येव चाभाष्य सारथिं तमभीक्ष्णशः।
हंसमत्तस्वरश्श्रीमानुवाच पुरुषर्षभः।।
O Rama, best among men with a voice resembling that of an intoxicated swan, called the charioteer again and again and said:
It is mentioned in Mahabharata, Vanaparva , Chapter 3 verse 13
कथं कुरुणामृषभ: स तु राजा युधिष्ठिरः ।
विप्रार्थमाराधितवान् सूर्यमद्भधुत दर्शनम् । ।
