Hurin, according to the index at least was called Hurin the Strong (as well as the steadfast), which would match up with Beleg Strongbow. (whereas Hurin the Steadfast doesn't really match up with Beleg Strongbow in my opinion.)
However I can't find Hurin the Strong in the main text anywhere.
Furthermore, you asked us to explain where the nicknames came from.
Although I seem to remember some sort of explanation of why Beleg was called Strongbow somewhere (at one of the bigger battles?) I haven't found it, nor of course an explanation of Hurin the strong.(The Steadfast is fairly obvious.)
As you asked the question, can you enlighten us as to the origins of the names? (or leave us longer to find them ourselves.)
Oh, I just wanted the word thalion... the word that both Hurin Thalion and Beleg Cuthalion have in common. I don't know all of what Tolkien intended, but thalion sort of looks and sounds like the lion. Hurin the lion. Strong. Steadfast. Tolkien sort of did the same thing with Mordor... and murder.
In The Silmarillion, Quenta Silmarillion, Chapter 21, Of Turin Turambar, both Thingol and Melian address Beleg as Cuthalion. He was one of the chief March Wardens of Doriath. Beleg had already unleashed Anglachel, the Black Sword, in his battles in Dimbar, but it is telling that in his stay among the outlaws that the land became known as "Dor-Cuarthol, the Land of Bow and Helm." Turin wore the Dragon-helm of Dor-lomin and Beleg bore the great sword Anglachel, yet the land was not known as the Land of Sword and Helm. Even though he had a famous sword, Beleg's prowess as a bowman is how he was known. Strongbow.
And in the paragraph where Beleg came to Amon Rudh, the text says... "And because Beleg was strong and enduring...."
As for Hurin in The Silmarillion, Quenta Silmarillion, Chapter 18, Of the Ruin of Beleriand and the Fall of Fingolfin, Hurin is described as "great in mind and body" and "tireless and enduring in body" at the Dagor Bragollach.
And later in Chapter 20, Hurin is the chief captain urging the Noldor and the Edain to stick to the battle plan. Dauntless. Of the reaguard action during the Nirnaeth Arnoediad, the text says, "of all the deeds of war that the fathers of Men wrought in behalf of the Eldar, the last stand of the men of Dor-lomin is most renowned. Steadfast.
Near the end of Chapter 20, "Hurin was brought before Morgoth... but Hurin defied him, and mocked him. Then Morgoth cursed Hurin and Morwen and their offspring, and set a doom upon them of darkness and sorrow... but it is not said that Hurin asked ever of Morgoth either mercy or death, for himself or for any of his kin."
The fifth paragraph of Chapter 21has the first mention of "Hurin the Steadfast." And thalion is first linked to Hurin by Gwindor at Eithel Ivrin, "Awake, Turin son of Hurin Thalion."