Some people might have found it kind of offensive, but Bucky was taking the risk that Tony wouldn't. Even though they had their differences, Bucky didn't think the guy took himself overly seriously. Other things, sure, but not something like a goat being his namesake. It was absurd and silly, which was what made it so funny -- at least, in Bucky's opinion. Not to mention, he wouldn't put it past Tony Stark to bleat at someone really loud if they were trying to get him to do something he didn't want to do or to just make them go away.
"If you met him you'd see why," he said. "I'm sure of it." Bucky was glad to see that Tony was being a good sport about it. That had been his hope when he revealed it to him. It was going to get out eventually, so Bucky figured he'd tell him himself. "He's even got this," he raised his human hand to his face and kind of rubbed his chin to indicate Tony's facial hair situation, "kind of going on. All he needs is some sunglasses. Maybe a band t-shirt and he can probably fill in for you if you need to take a day."