Calling the children girl and boy is probably the worst thing she could do...

From a psychological perspective, not giving the children names could scar them for the rest of their lives... Those kids are old enough that, when they finally DO get names, they'll feel foreign to the kids, and they'll resist using it, or being referred to as anything other than "boy" or "girl." And it will take longer for them to actually get used to responding to their name being called instead of boy or girl, because it's easier to imprint matters of "who am I" on younger kids than on older ones... Also, down the line at some point, they'd really start to question, 'Is THIS my real name or was mom lying about THAT too?' Super trust-issuey.
I totally get why she didn't want to name the kids but... the alternative presented in the movie is way worse from a psychological perspective...