Final answer:
Bilbo uses riddling talk with Smaug and gives himself the titles "Barrel-rider" and "Ringwinner," which refer to his adventures in 'The Hobbit.'
Step-by-step explanation:
When Bilbo Baggins interacts with Smaug in "The Hobbit," he uses clever wordplay and gives himself various titles rather than stating his real name directly. Two of the titles he gives himself are "Barrel-rider" and "Ringwinner." "Barrel-rider" alludes to the method by which he and his companions escaped from the elves, and "Ringwinner" refers to his acquiring of the ring from Gollum. The use of these clever titles serves to intrigue Smaug and to protect Bilbo's identity, showcasing Bilbo's resourcefulness and quick thinking.