Because the Rishi Vasishtha had determined to kill himself, but had refrained from doing it as soon as he heard of the conception, the child (when born) was known in the world by the name of Parashara.
परासुः स यतस्तेन वसिष्ठः स्थापितो मुनिः। गर्भस्तेन ततो लोके पराशर इति स्मृतः॥