The Septuagint Book of Job includes scribe's report that Job and Jobab were the same person, with Jobab being a name Job used earlier in life. According to Emil Hirsch in the Jewish Encyclopedia:
In the Greek version of the Book of Job, at the end, there is the
following addition: "This man (Job) is described in the Syriac book as
living in the land of Ausis, on the borders of Idumæa and Arabia; and
his name before was Jobab; and he, having taken an Arabian wife, begot
a son whose name was Ennon. And he himself was the son of Zare, who
was one of the sons of Esau, and Bosorrha; so that he was the fifth in
descent from Abraham. And these were the kings who reigned in Edom,
which country he also ruled over: first Balak, the son of Beor, and
the name of his city was Dennaba; and after Balak Jobab."
This is convincing evidence for those who accept the Septuagint as inspired scripture even when it departs from the Hebrew version in a major way. However, for those who see the above as a scribal insertion, the proof is not convincing. The Syriac version of Job available at Biblehub.com does not contain the above quotation. The report does exist in the Septuagint but it is clearly the work of a scribe, who states: Οὗτος ἑρμηνεύεται ἐκ τῆς Συριακῆς βίβλου - "This is interpreted from the Syriac Bible."
The quote does show that the identity of Job and Jobab was a credible enough idea among to be included in the Septuagint version of the Jewish Bible. Those who accept the Septuagint as authoritative will find this convincing. Later Jewish theories about Job's identity from the rabbinic period are discussed here.