This seems to be a minority opinion, but:
According to Mordekhai (Kiddushin 533, to Kiddushin 65b (page 4a in
the Vilna Mordekhai; he cites Rabbenu Barukh), a couple who lives
together and eidim see them have relations, even without any legal ceremony requires a get upon
Source: this page, which adds: "This is an oft-cited opinion, but in reality, he is in a significant minority. Very very few poskim agree with him about this."
These are the words of the mordechai:
פסק רבינו ברוך הבא על הפנויה וראו עדים דצריכה הימנו גט דאמרי אין אדם עושה בעילתו בעילת זנות ואם בא עליה בעדים אדם אחר צריכה גט משניהם ומיימוני פליג
Rabeinu Baruch says Someone who cohabits with an unmarried girl and 2 witnesses saw, she needs a get since we say a person doesn't have relations for the sake of immorality, however if another man had relations with her Both of them need a Gett (divorce), this is because we are not sure of the motivations so in case of doubt both men need to give a gett. The Maimonidies (Rambam) argues that no Get is needed.