I feel like if the LW was saying, "this is such a charming kid, would it be okay for me to hang out with them and bond over the cat?", my answer would be, "absolutely but still be prepared to set boundaries."

I feel like learning your adult neighbors' names in this circumstance is not too much to ask--in fact I routinely make new neighbors banana bread/brownies/etc. and bring them over and introduce myself, writing in a little greeting card that says, "Welcome to the neighborhood!--your neighbors at [street number], Marissa, Mark, and Tim." When tinydog was still alive I wrote, "Marissa, Mark, Tim, and Ista (dog)." So I feel like learning adult neighbors' names and telling them yours is well within bounds if you want to. The other people in my house are not mad that I tell the neighbors their names but do not have the impulse to introduce themselves. I think there needs to be room for both. But going from "I don't know the parents' names" to "I have their kid over daily or for an hour at a time" is a big change; if LW was inclined to befriend the kid I would expect LW would at least have introduced themself to the parents.