Hal, maybe you’re right. But I feel like I recommend against making the mention of “Skywalker” be the thing that causes Rey to look at the kids - she looks at the kids in the first place because they are what she and the Resistance are fighting for.
The movie is called The Rise of Skywalker…
The scene immediately afterwards she is asked for her “family name”.
The whole puppet show and surrounding scene is used to help reinforce the ending of the film and actually make Rey’s name change feel earned.
Rey reacting to “Skywalker” helps to show that the spark that will ignite the fire that will burn down the First Order because of Luke’s sacrifice is still alive and it is worth it for her to continue fighting and accept being a Jedi. Because THAT’S what she and the Resistance are fighting for.