This incident made a deep impression on the King. He realized that the power obtained by penances was far greater than mere physical might. He renounced his kingdom and began his quest to become a greater rishi than Vasishta. He took on the name Vishwamitra. It is very interesting to see all the challenges that Viswamitra faced in his life to become a Brahmarishi, before eventually giving up the greed to possess the cow. After many trials and undergoing many austerities, Vishwamitra at last obtained the title of Brahmarishi from Vasishta himself. During this time he had a daughter named Shakuntala (who appears in the Mahabharata) with Menaka, an apsara in the court of Indra. Son of Shakuntala became a great emperor. He came to be known as Emperor Bharata, in whose name the land of India got its name Bharat.
 Alternate version
Kaushika seeks to attain the same spiritual power as Vasishta, to become his equal, a brahmarishi. He undertakes a fierce penance for one thousand years, after which Brahma names him a Rajarishi, or royal sage.
After another long penance of ten thousand years, Brahma names him a rishi, thus leaving his royal lineage permanently.
At this point, Indra, the king of Swarga attempts to test the tapasvin by sending Menaka, an apsara to seduce him. Kaushik then lives with Menaka for 10 years. They have a baby girl Shakuntala. Kaushik becomes angry as Menaka had destroyed his years of meditation and thus he cursed her that she won't possess her beauty, of which she was proud, in next birth. And hence in the next birth she became a monkey and mother of Hanuman, Anjani.
Kaushika now goes to the banks of the river Kaushiki, which is the spirit of his own sister. After many thousands of years of penance, Brahma names him maharishi, but also tells him that he hasn't become a jitendriya yet, lacking control over his passions. This is brought to light to Kaushika when he angrily curses Rambha, an apsara sent by Indra to seduce Kaushika again, to become a stone for a thousand years.