Yes. Papua New Guinea occupies the eastern half of the island of New Guinea.

Papua New Guinea/ New Guinea's official name is Independent State of Papua New Guinea.

What is north of Australia with dense forest

No, Papua New Guinea is in the Pacific. It is the country on the eastern half of the island of New Guinea, although it is sometimes called New Guinea for short. The western half of New Guinea is Indonesian territory. Papua New Guine and New Guinea are completely different to the country of Guinea (officially the 'Republic of Guinea') in west Africa.

Papua New Guinea is a country on the island of New Guinea.