What was east Timor renamed to?

East Timor was renamed to Timor-Leste, which means "East Timor" in Portuguese.

When did it gained independence and who was it's first PM?

Timor-Leste gained independence on May 20, 2002. The first Prime Minister of Timor-Leste was Mari Alkatiri, who served from 2002 to 2006.