It is interesting to unpack this statement in 2 Kings. First this statement:
To this day they persist in their former practices. They neither worship the Lord nor adhere to the decrees and regulations, the laws and commands that the Lord gave the descendants of Jacob, whom he named Israel. When the Lord made a covenant with the Israelites, he commanded them: “Do not worship any other gods or bow down to them, serve them or sacrifice to them. But the Lord, who brought you up out of Egypt with mighty power and outstretched arm, is the one you must worship. To him you shall bow down and to him offer sacrifices. You must always be careful to keep the decrees and regulations, the laws and commands he wrote for you. Do not worship other gods. Do not forget the covenant I have made with you, and do not worship other gods. Rather, worship the Lord your God; it is he who will deliver you from the hand of all your enemies.”
The assumption clearly at the heart of "whom he named Israel" (אֲשֶׁר-שָׂם שְׁמוֹ יִשְׂרָאֵל) is that it was God himself who wrestled with Jacob. When you think of it, this interpretation may be the simplest interpretation of Genesis 32 but it has obvious difficulties (i.e. God is anthropomorphic, Jacob defeated God etc). To this end it is intriguing to see the early Christians engage in the same kinds of debates as the early Israelites viz. the accusation that the Samaritans were 'idolaters' for suggesting there were two gods.
In other words, we can presume that the 'Samaritans' (the ones argued to have been influenced by the idolatry of Kutha) argued that Genesis 32 can't be depicting the Almighty God wrestling and losing to Jacob. This is clearly stupid and debases the god of Israel - but more importantly that is the Samaritan reading today. Nevertheless it necessarily means Israel was not monotheistic - something more explicit in the use of more than one divine name. I read 2 Kings then less in terms of a slight against Samaritans (which is still present in the text) but rather part of an overarching rejection of 'orthodoxy' at that time based in Samaria. In other words, it seems absurd to suggest that Ezra or whomever wrote the Pentateuch intended to depict the Almighty God of the universe as losing a wrestling match with Jacob. This couldn't have been the original meaning of Genesis 32. Nevertheless the author of Kings perhaps in the fourth century was part of an early monarchic effort centered in Jerusalem to - on the one hand - present the story of Israel 'as if' it were about one God (something plainly contradicted by the use of more than one divine name etc) and moreover argue on behalf of a single divine monarchy that fulfilled the 'expectation' of the Pentateuch.
Remember, there is nothing in the Pentateuch which 'looks forward' to a monarchy. The Pentateuch is a document written by priests and for priests. There is no command to build a permanent temple. All that is proscribed is a flimsy 'portable tabernacle.' The point here is that if you just read the Pentateuch you would simply arrive at the conclusion that God only wanted a priesthood carrying out its duties in a portable tent. The author of Kings is necessarily presenting the Judean monarchy as the 'fulfillment' essentially of the Pentateuch even though the Pentateuch doesn't not ask for the raising of a kingdom, it doesn't look forward to it.
How do we know that the author of Kings presents the Judean kingdom in this way? Because the years of the Judean kingdom add up to 345 years a number which equals Moses. The same argument has been used by Samaritans to justify that a man named Mark (Marqa) was the ultimate exegete of the Pentateuch. Moses says that 345 will come in the future. For the author of Kings - or better yet the document 1 and 2 Kings presents the Judean kingdom (the ultimately fictitious portrait of the Judean monarchy in the past) as that fulfillment. It presents the years of the kingdom of Israel as 209 which = 'other' in Hebrew a terms which denotes 'the second class, the one one who comes behind, after' the kingdom of Judea. The point of course is that the primary difference between the Jews and Samaritans in the Second Commonwealth period is that the Samaritans had no messiah, no expectation for a king who would come after Moses. Why is this? Because it isn't in the Pentateuch, none of this in the Torah.
I have to suppose that the one idea led to the other - viz. that the Jewish interest in establishing a political monarchy prompted the writing of the pseudo-history of Kings. In other words, it must have been written in a time period when Jews were actively seeking to demean the traditional understanding and interpretation of the Pentateuch which was entirely apolitical. It was clearly a priestly doctrine by and for priests. The chiding of Samaria in 2 Kings - the accusation that their doctrine of a second god who wrestled with Jacob and named Jacob Israel was shaped by foreign influences - is in fact a way of saying that their apolitical doctrines by and for priests was not the true interpretation of the Torah (which of course it was).
We can of course get a glimpse into what the author of Kings was 'seeing' in the accusation that the traditional understanding (i.e. the Samaritan understanding) was tinged by contact with the 'idolatry' of Cutha. He is essentially saying that the second god of the Samaritans is really a worship of Nergal. This makes some sense when you think about it as you see the second god appear in fire in Exodus 3 and again on top of Sinai in the theophany. Yahweh is similarly a war god in Exodus 15. in fact one can argue that the god who manifests himself in Exodus is a lot like Nergal. Now of course this is a dangerous accusation insofar as both Jews and Samaritans had basically the same text. If you make the argument that the destructive war god who appears in fire is not the second god to a more powerful omnipotent divinity who is heard from heaven (not seen) in the theophany on Sinai you could still make the case that this one and only god was influenced by Nergal. He still has the same attributes. Nevertheless I suspect that the Israelites (both Jews and Samaritans) already had a strong notion that there was one all powerful ruler of the universe distinct from the gods of the pagans. I think it is in this context that the idea of a 'second god' is so offensive. The hatred of foreigners is what drove monotheism.