I think the first recorded person named Shoshana is in the sefer hitzoni “Megilat Shoshana”. The sefer was included as perek 13 in Sefer Daniel in the Septuagint (obviously not in our Daniel and not found in the Dead Sea Scrolls Daniel fragments). It is an interesting story about a woman named Shoshana Bat Hilkiya wife of Yehoiakim, accused of adultery and saved by a young Daniel who finds contradictions between the testimonies of her accusers.
The sefer is not mentioned explicitly by early Chazal but seems to be what the Ramban is referring to in Devarim 21:14 as “Sefer Shoshan”. Hope this helps