Kaushika/Koushika/Kaushik is a surname found in Brahmins. Origin of Kaushika can be referenced to an ancient Hindu text. There was a Rishi (saint) by the name of "Vishvamitra" literally meaning 'friend of the universe','vishwa' as in universe and mitra as in 'friend', he was also called as Rishi 'Kaushika'. Vishvamitra is famous in many legendary stories and in different works of Hindu mythology.
Read more about Kaushik: Kaushik/Vishwamitra Gotras, Gayatri Mantra, In The Ramayana, Origins, In The Rig Veda