"It's going well so far. One of my rare moments to myself, so I decided to make the most of it." Castiel wasn't accustomed to having many moments to himself. So he was unsure of what to do that particular day. But at least he had some time to himself for a change.
"My name is Castiel," he offered. Why is parents had named him Castiel was beyond him, but that's the name he had been given. He'd adjusted to the strangeness of his name. And the looks he received when people realized it was his actual name and he wasn't trying to pull one over on them.