The Tzedukim didn’t take the advice of the guy Popa mention — to start from scratch. They put on Tefillin, because everyone always put on Tefillin. Then they made the changes whenever they felt that the Chachamim injected their own desires and worldview.
They didn’t call themselves Perushim because they called themselves Yehudim. Perushim is a title created by outsiders, who wanted normal Frum Yiddishkeit to be a certain sect within Judaism. The only time we find Chazal referring to themselves as Perushim is when they quotes Tzedukim.