Fifteen years of having a voice back didn't mean Jarvis was accustomed to using it with strangers. For the first five or more, he'd only spoken to Tony, and only within the familiar confines of their home; first careful questions about meals, preferences, household tasks and that sort of thing, and then branching into the way they spoke to one another now (also rarely witnessed by anyone, because Jarvis wasn't comfortable enough to go spouting off or rolling his eyes around even the few people who knew him to be capable). It felt... vulnerable, exposing this. Part of him had seized up in the face of Rogers' wide-eyed shock, but he was trying not to look too cowed. Tony was already visibly uneasy, and poking too hard at tension that way would lead to unfortunate results.
Discomfort and Tony in most combinations resulted in verbally lashing out at the least, which wouldn't help this situation. Instead, Jarvis forced a deep breath around the apparatus fitted to his mouth- no longer a tablet on which he typed, the interface expanding and growing more user friendly over the years because Tony never stopped even when Jarvis assured it was fine and functional and more than anyone else got to have- and reached to carefully take the hand he was being offered.
Peculiar, the gesture. He'd never been given the opportunity for actual introduction before. Clint, who knew he could talk, had gotten a far less formal glimpse into Jarvis' abilities and that had been that. Rogers- Steve, he'd offered- seemed nothing short of genuinely pleased to be able to hold out his hand and name like Jarvis was any other person he'd encountered, worthy of manners. It was endearing, but he'd said as much to Tony already. Steve was the kind of man that inspired others by easy charisma alone.
"Jarvis," he replied, accompanying the name with a small but sincere smile. "Thank you for coming back. I was... concerned after your last visit that we might not have another opportunity, and Tony's correct. We know what's at stake. We'd like to help." There. Simple and unvarnished and true, and Jarvis slipped back a step after a quick shake of Steve's hand, occupying space near Tony again; not touching, but close enough to feel less exposed.