"We will begin collecting public suggestions starting today and change the party name as soon as possible," said party chairman In Myung-Jin.
The Saenuri, or New Frontier, party was formed from a merger of several centre-right parties in 1997 and known as the Grand National Party until 2012.
Park changed its name as part of an attempt to reform and regain voter support ahead of that year's general elections, which it won.
But a swirling corruption scandal has surrounded Park, centred on her confidante Choi Soon-Sil, with huge demonstrations demanding her resignation, and she was impeached by parliament last month.
The country's supreme court is currently deciding whether to uphold the move. If it does so new elections must be held within 60 days.
Saenuri said most of its members supported a change of name, calling it the only way to give the party a "new life".
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