In The Hobbit, what name does Bilbo give his sword and why?

Ok Orcs have nothing to do with why Bilbo named it Sting, and while it is of Elven make it's not made of Mithril as only the Dwarves worked with Mithril. Sting is named wholly because of Bilbo's encounter with the spiders

"Somehow the killing of the giant spider, all alone by himself in the dark without the help of the wizard or the dwarves or of anyone else, made a great difference to Mr. Baggins. He felt a different person, and much fiercer and bolder in spite of an empty stomach, as he wiped his sword on the grass and put it back into its sheath."
"I will give you a name," he said to it, "and I shall call you Sting."