Abbas says this will happen in about a year at the most, replacing the name Palestinian Authority.
He spoke after talks with Greek Prime Minister Alexis Tsipras. Abbas arrived in Greece on Sunday, and is due to address the country's Parliament tomorrow.
The parliamentary Foreign Affairs and Defense Committee has unanimously called on the Greek government to recognize Palestinian statehood.
Tsipras' leftist-led government is trying to balance improved relations with Israel with his party's longstanding support for a Palestinian state. Tsipras visited Israel last month, meeting with Prime Minister Benjamin Netanyahu. He also met with Abbas in Ramallah, West Bank.