How does Bilbo's newly named sword relate to his new self and why doesn't Bilbo want to reveal the ring to the dwarves?
Up to the point where Bilbo kills his first spider and names his sword Sting, Bilbo has not done one heroic deed on his own. Previously, every time the company got in trouble, it was Gandalf who guided the company through. When Gandalf left the party after the rest at Beorn's, he put Bilbo in charge of the expedition to Lonely Mountain. Gandalf knew that deep down inside Mr. Baggins was a Took part of him longing to come to the surface. The Tooks were an adventurous and brave family of Hobbits, which had led to them being known as not respectable among the peace loving Hobbits in the Shire. The Baggins is one of these respectable families. Bilbo is half Took and half Baggins, but he has led his life, up to this point, as a peace-loving Baggins. With the death of the spider, Bilbo's Took side comes forth, and he has now become an adventurous, brave Hobbit.
After his escape from Gollum, Bilbo overhears the dwarves quarreling about the loss of their burglar to the Goblins. He leaves the ring on and, because Hobbits can move very quietly, he creeps up on the dwarves before removing his ring to reveal himself. Because he was able to do this, the dwarves' praised his burglar skills. Basking in their praise, Bilbo kept the secret of the ring to himself.
When Thorin and company come into the presence of the Master, the raft-men of the elves told him that they were the Elvenking's escaped prisoners.
Giving a name to anything helps to transform it. Naming your car, a boat, a house--gives it an importance not there before and this flows over to those who own these items. Bilbo's character is a mite selfish...this is why he is reluctant to tell the dwarves of the ring. It's awesome what the ring can do...he understands the danger and what his mission is, but that doesn't keep him from wanting to keep the "precious" for himself. Look for the other answers to your questions in the study guide here at enotes for this amazing book. Good Luck!
Bilbo, when we first meet him, is a weak and passive character. He allows others - namely the dwarves - to invade and take over his life. He doesn't want to go on the adventure, but he is unable to stand up for this, or to express himself in an effective manner. However, as the story continues, Bilbo begins to take action. He becomes a theif, a rescuer, and a skilled con artist. The word "sting" represents the new active side of Bilbo.