The tribe of Judah is properly referred to as “Jews or Jewish”, whereas Israel refers to all of the tribes. Throughout the history of Israel, though, the name Israel and Judah gets interchangeably used:
The earliest known mention of “Israel” comes not from a Jewish text, but from an Egyptian one: the Merneptah Stele, dated to around 1200 BCE. This inscription records a military campaign in the Southern Levant and refers briefly to a people called “Israel.”
Scholars debate who exactly these people were, and it remains unclear whether they included people who later came to be known as Judahites – the ancestors of today’s Jews.
During the subsequent Iron Age (around 1130–586 BCE), appearances of the term “Israel” slowly begin to increase in the archaeological record, but always with reference to the northern kingdom centered in the region of Samaria. Meanwhile, the southern kingdom, centered in Jerusalem, is consistently known as “Judah,” and its people as “Judahites”. Israelites are in the north, Judahites in the south.
These Judahites are never depicted as part of a larger nation of “Israel.”
The northern kingdom of Israel fell to the Assyrians in 722 B.C.E., and many (but apparently not all) of its residents were carried off to exile in Mesopotamia. After this, the name “Israel” fades for a time from the inscriptional record, while the name “Judah” and its derivatives continue uninterrupted. source: https://www.haaretz.com/archaeology/2025-04-30/ty-article/when-did-jews-begin-calling-themselves-israel/00000196-853a-d22a-a3de-b53e117d0000
Not relying on the Bible for explanation, the article might deduce that when the tribes split from Jerusalem that the Northern tribes referred to themselves as Israel, and began to worship the golden calves, whereas the Southern side probably began to be referred to as Judeans. The original break in this matter involved taxes, and the Northern tribes felt that the taxes being charged by Rehoboam, Solomon’s son, were too high. Hence, the internal strife sewed division, and when the internal strife was not present there was only Israel, which naturally included Judah as that appellation referred to all tribes.
The article slowly and painfully arrives at the above conclusion:
In 332 B.C.E., Alexander the Great conquered the region and ushered in the Hellenistic period. From this time onward, the name of the former province of Yehud was rendered into Greek as “Judea”, and its residents and diaspora communities associated with it became known as “Judeans”.
Greek inscriptions on stone and papyrus consistently refer to them as Judeans, never as “Israelites.”
The name “Israel” re-emerges again on a Greek inscription from the Aegean island of Delos, dated between 250–175 BCE. It refers to “Israelites” worshipping at Mt. Gerizim – suggesting that these were people hailing from Samaria rather than Judea.
This important inscription suggests that the title “Israel” was preserved by descendants of people who lived in the northern kingdom for several centuries after the fall of Samaria.
So when did Judeans begin identifying themselves as “Israel,”and why? The answer appears to lie in the Hasmonean period, the short-lived era of Judean independence which followed the Maccabean revolt against the Seleucid (Syrian) Greeks in the 160s B.C.E.
It is from this time that evidence begins to emerge in the archaeological record indicating that Judeans were observing the laws of the Torah. And it is from this time that scholars date the bulk of the earliest Biblical texts among the Dead Sea Scrolls.
The Hasmoneans appear to have adopted both the Torah as state law and the Biblical origin story of Israel as their national myth. According to this myth, Judeans have always formed an integral part of a broader nation of “Israel”. source: ibid
Or, in other words, the Maccabees purged Israel of a lot of Greek influence, and placed the nation back on a Biblical foundation, which the article refers to as “myth”, and by so doing, was able to forge the identity of Israel being composed of both Judah and all the other tribes.
All of this seems like some special wrangling for claims that the Bible easily elucidates, but then again, the testimony coming from several directions might help strengthen the facts the Bible outlines for those that require them.