The name Yahweh appears frequently in the Old Testament, being usually translated LORD in the King James Version, the New King James Version, the New International Version, and others. It appears with the following frequency in the Pentateuch: Genesis 149, Exodus 371, Leviticus 302, Numbers 381, and Deuteronomy 539. There is no decline of frequency throughout the OT.
Throughout the OT Yahweh is the God particular to the Israelites: on the face of it it seems very odd that they should take their God from any tribe or nation. In their own minds, it was their God which identified them as a unique people amongst the nations. How could such a situation have arisen if their God was actually taken from some other nation?
The first archaeological attestation of the name is from the Soleb Inscription in Sudan of Amenhotep III who reigned 1415-1377 (high chronology):
The inscription speaks of "the Shasu of Yahweh" as being the enemies of Egypt, and it is clear from the layout of the inscription that these enemies are geographically to the north or north east of Egypt. "Shasu" is a broad term meaning nomads, or wanderers, but I think can more broadly mean foreigners. It would be a mistake to try to pin down the term to either the Israelites or the Moabites or to any other people group.
If the Wellhausen Documentary Hypothesis is to be believed then the Pentateuch was written centuries, nearly a millenia, after the period. Clearly in such a case the Pentateuch need not be taken seriously as history.
In the 1940s Edwin Thiele produced his doctoral thesis which explained how the years of the kings in the books of Kings and Chronicles stacked up. It is usually supposed that until his thesis the length of the reigns had largely remained a mystery. But in point of fact Valerius Coucke a Belgian Priest had already cracked the code of when the Hebrew kings reigned in the 1920s. See the fascinating wikipedia article "Valerius Coucke" which gives a good description of his methodology, etc. Edwin Thiele's thesis led to the book "Mysterious Numbers of the Hebrew Kings". Both these men put the time of the start of the building of Solomon's Temple at 968/967 BC.
One difference between the two men was that Coucke thought that Jerusalem had been destroyed in 587 BCE whereas Thiele thought it had been 586 BC. Rodger C. Young subsequently found what appears to be a mistake in Thiele's work... Jerusalem was destroyed 587 BC.
If 967 BCE is taken as the year of the beginning of the building of Solomon's Temple then 1 Kings 6:1 puts the year of the Exodus from Egypt as 1446 BC.
It is important to realize that the reign lengths in Kings and Chronicles had perplexed Bible students for centuries. In the first or second century a Jewish author had produced a work on Bible chronology called the "Seder Olam". In this the author shows his confusion at the reign lengths.
Subsequent to the work of Edwin Thiele it was found that the date of the Exodus can also be determined from a right understanding of Ezekiel 40:1. This verse speaks of "Rosh Hashanah", New Year's Day, happening on the tenth of the month in the 14th year after the destruction of Jerusalem. Rosh Hashanah usually happened on the 1st of the month, but every 49 years, in the Year of Jubilee, it happened on the 10th of the month, in accordance with Leviticus 25:9. The problem for those who subscribe to the Wellhausen Documentary Hypothesis and any of its derivatives is that the Seder Olam says that the Jubilee which is mentioned in Ezekiel 40:1 was the seventeenth Jubilee Year. The critical section reads:
And so it says (Ez. 40:1): "In the 25th year of our exile, on the day of the New Year, on the tenth of the month, 14 years after the destruction of the city [of Jerusalem]." When did he [Ezechiel] have this vision? At the beginning of a Jubilee period. If they stayed for 17 entire jubilee periods, how can there be an excess of 17 years? (See Chapter 11,"Conquest of Joshua", of Seder Olam online; for example: https://www.bible.ca/manuscripts/Seder-Olam-Rabbah-full-text-PDF-Free-Online-Chronology-modern-Jewish-calendar-Textual-variants-Bible-manuscripts-Old-Testament-Torah-Tanakh-Rabbinical-Judaism-160AD.htm#pdf )
The author of Seder Olam is trying to make sense of the chronology. It is not important to us that he is confused. What is important is that he speaks of 17 entire Jubilee Periods: he had access to this information which was almost certainly stored by the priesthood at Jerusalem.
17 Jubilee cycles means that 833 (17 times 49) years had elapsed since the Israelites had entered the "Promised Land". Since Jerusalem was destroyed in 587 BC, the 14th year after this was 574 BC and (16*49 + 50) years before this was 1406 BC. Adding 40 years for the period the Israelites wandered in the wilderness gives 1446 BC, precisely the same year as that calculated by Valerius Coucke, (and Rodger C. Young and Andrew Steinmann today). And the real problem is compounded by the fact that, for the Jubilee Years to have started from the entry into the Promised Land in 1406 BC, the Book of Leviticus which gives the regulation concerning the cycle of the Jubilee Years must have been written previously to 1406 BC. The Book which contains priestly information, which the Wellhausen Documentary Hypothesis says was written last, was written before 1406 BC. For more information on this see the paper on rcyoung.org/papers.html "2008c - Evidence for Inerrancy from a Second Unexpected Source: the Jubilee and Sabbatical Cycles" by Rodger Young.
Once it is accepted that the Pentateuch was written while the Israelites were in the wilderness the harmony and synchrony between the Bible data and the High Chronology for the 18th dynasty of Egypt becomes explicable... the author of the Pentateuch knew what he was talking about because he was writing about his own life and his own era.
Acts 7:23 and Acts 7:30 must have been written using sources which no longer exist but which were known in the first century. Moses was 40 years old when he killed an Egyptian task master and did not return to Egypt for 40 years. He returned to Egypt after the king who had sought to kill him had died (Exodus 2:15, 2:23 & 4:19). So we need to find a Pharoah who reigned 40 or nearly 40 years. The only candidates in the New Kingdom period are Thutmose III (1504-1450), Amenhotep III (1415-1377) and Rameses II (1290-1224). Obviously, the date of the Exodus of 1446 BCE fits Thutmose III. He was the king who tried to kill Moses; he died in 1450 BC, just four years before the Exodus; and Amenhotep II was the Pharaoh of the Exodus.
The other two kings, Amenhotep III and Rameses II, who I have supposed to have been possible candidates for wanting to kill Moses are ruled out on other grounds:
If Rameses II had been the Pharaoh who tried to kill Moses then the king of the Exodus would have been Merneptah. He reigned only 10 years, and yet his Merneptah Stele speaks of destroying the Israelite people in the Levant, when they, according to the Bible were not in the Levant but were still wandering in the wilderness of Sinai, 40 years.
If Amenhotep III had been the Pharaoh who tried to kill Moses then it makes no sense that the subsequent Pharaoh Amenhotep IV should have asked Moses "Who is Yahweh that I should obey his voice?" (Exodus 5:2) when Amenhotep III already acknowledges he knows about Yahweh on the Soleb Inscription in Sudan.
It was Amenhotep II, then, who ruled before Amenhotep III, who asked that question: by the time of Amenhotep III the Egyptians were all too familiar with Yahweh, the god of their enemies whom they called "the Shasu of Yahweh".
Why did Amenhopep II ask Moses such a question? The Egyptians were an exceedingly religious people. Archaeology has discovered that even the slaves had certain privileges given them by their Egyptian overlords. They had the right to worship their gods on the worship days of their gods. The Egyptians must have had officially produced lists of all the gods for whom each group of slaves enjoyed this privilege. On the list for each tribal group of slaves was the name of the god(s) they worshipped. And for each god were marked the day(s) of the year when the respective slaves were permitted to stop slaving away and to go and worship. What the Pharaoh was saying was "Your god Yahweh is not on my list!" The Pharaoh had never heard of Yahweh.
From the Louvre Roll it is evident that special religious holidays were granted to the workers, and work rosters from the workmen's village of Deir el-Medinah report men being off work "to offer to their god". This ... seems to indicate that Moses' request for the Israelites to have time off to worship Yahweh was not unprecedented and may have been standard procedure (Exod. 5:1). (James Hoffmeier - "Israel in Egypt", 1996, page 115).
Up to this point then the Israelites had not put in a request to worship Yahweh, if they had the Pharaoh would have known his name. The Israelites were not as yet worshipping Yahweh but were probably worshipping other gods such as the Egyptian goddess Hathor who it seems they recommenced to worship at the foot of Sinai.
The agreement of the two different ways of calculating the date of the Exodus give evidence the Pentateuch was written before 1406 BCE;
In Exodus 5:2, Amenhotep II had never heard of Yahweh, because the Israelites themselves had never ensured the name Yahweh or his worship was on Amenhotep II's list of gods for yearly worship; at that time the Israelites didn't worship Yahweh;
Later, the Israelites saw their worship of Yahweh as distinctive among the nations, it really does seem to be stretching it to suggest they learned about him from other nations;
But Amenhotep III had a stinging memory of Yahweh, he knew all about him. And how could he have described any group of people as "the Shasu of Yahweh" if several different peoples worshipped Yahweh and thus this description did not uniquely identify any particular body of people?
What better explanation is there than that Moses received the name Yahweh just prior to returning to Egypt as described in Exodus 3:13-15?