Kaushik (Hindi: कौशिक) or Kaushike (Marathi: कौशिक) or Koushik/Kousik is a surname and gotra of Brahmins named after Brahmarishi Vishvamitra.
Origin of Kaushik 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 "Kaushik".
Vishvamitra is famous in many legendary stories and in different works of Hindu literature.
[3] The name "Koushika" (i.e. Kaushik) literally means "descended from Kusha".