Tony had told Pepper that Bruce was coming, his best friend from back at MIT. She knew about the trial. Who didn't? She had always thought he was guilty, but it didn't seem like Tony really wanted to talk about it so she didn't bring it up. The man had been off the grid for so long he may as well been in jail. She gave Bruce a smile and got up to introduce herself.
"Hello," she said. "My name is Pepper. It's a pleasure to meet you." He didn't seem to get the whole hand shaking thing, so Pepper just hung her hand awkwardly in the air and then looked all-too-thankful to see Steve walk in and interrupt the awkward. "Steve!" she exclaimed. "It's so good to finally meet you," she said, offering him a hand.
When Thor and the dog came in she had mixed feelings. She was more of a cat person, first of all, but also a dog could make a hospital BBQ very... interesting. She eyed the dog warily, but then decided to just ignore it and introduced herself to Thor instead. "I'm Pepper," she said. "This is Tony and Natasha and Bruce and Steve," she said, indicating to each person as if she was introducing everyone to everyone else.