Here's a breakdown of the significance:
* From "Orcrist" to "Sting": The original name, "Orcrist," is a menacing and powerful name, reflecting the sword's true nature as a weapon forged for battle. Bilbo, at the beginning of his journey, is timid and hesitant, not comfortable with violence. He initially avoids the sword, seeing it as something dangerous and alien. Renaming it "Sting" reflects his newfound confidence and his acceptance of the weapon's role in his survival.
* From "A Little Knife" to "Sting": Bilbo initially considers the sword as a mere "little knife," underplaying its significance and his own emerging bravery. By calling it "Sting," he acknowledges its sharpness and power, and the role it plays in his protection.
* From Fear to Acceptance: Bilbo's decision to rename the sword signifies his growing comfort with his role in the journey. He is no longer just a "burglar" or a "hobbit" who stumbled upon a quest; he is a participant, a warrior who needs a weapon to fight for his survival.
* From Hesitation to Proactivity: Naming the sword implies a sense of ownership and control. While initially hesitant, Bilbo is now actively using and claiming this weapon as his own. This proactive approach marks a shift in his character, moving him from passive observer to active participant in the dangerous world he has entered.
* From Individual to Part of a Team: The act of naming the sword "Sting" is also a symbol of his growing integration into the company of dwarves. He is no longer just a hobbit on his own, but a part of a team, and he is now ready to face the dangers with them.
The renaming of the sword is a subtle, but profound, reflection of Bilbo's character development. It highlights his journey from a timid, reluctant hobbit to a brave, resourceful adventurer who is willing to confront his fears and embrace his role in a world far greater than his own.