The reason Kay introduced them using their codenames first, was because that was the effect she wanted to have on them.
It showed just how unique and special Lianne is, and knowing her team, they would understand immediately. They would be curious but they wouldn't ask. What was important was that they now know Lianne was not just someone Kyle was sponsoring.
Since Joseph didn't come, Kay could do so, thus she felt it was perhaps best that he didn't come after all.
Though she felt a bit sad at the thought and wondered why she had been hit with that emotion when Joseph looked indifferently at her and went back to playing games.
Thinking about it, it was a normal reaction, right?
What teen boy would find going to the office as interesting? Especially when he had that dream gaming set-up in his bedroom?
What wasn't normal was her sadness and disappointment at his reaction.