Misato:“Just ‘Misato’ is fine. Pleased to meet you, Shinji Ikari*.”
* Ikari Shinji-kun
Reichu: Misato gets some very “bouncy” (i.e., perky) character animation in this episode. I find it a visual confirmation of the overall image Misato gives when we first meet her, as this extremely casual, upbeat woman.
HeWhoPostsStuff: Makes it all the more shocking to the viewer when we get to see her in her “natural habitat” later on…
Kendrix: Note how the uncovering of her eyes coincides with her recieving a Name, unveiling them along with her identity and the fact that she seems to be nice. And of course, our cute little protagonist gets a name, too. Ikari Shinji. Now, most the surnames in this show are fairly odd because there's a nautic theme naming going on - when the names aren't taken from WWII ships, they're taken from random ship related terms. The last name means "anchor", but is homophonous with the japanese word for "wrath". As we find out soon, both this name and, yes, the berserker rage it implies are hand-me-downs from his mommy, even if neither of them really look the part.
As for his first name, it's very common, Japan is filled to the brink with Shinjis, but it also means "divine child" which is perfect for a chosen one who looks very ordinary/not chosen-one-y at all on first glance.
At this point, we can expect those two to more or less bond over the course of the series, she immediately tries to present herself as someone who isn't all stiff and formal and can be talked to,