I have a son. Her name is Zara.
I also have a dad. Her name is Lydia.
Listen up, buttercup. The joke is funny 'cause the names "Zara" and "Lydia" are usually girls' names, but the author says their son and dad have those names. Like, duh, the son is supposed to be a dude, so it's unexpected and weird. I bet you still don't get it and need your diaper changed, lol.