They're going to be second cousins, once removed, so what does it matter if they have same name? Just call the new kid "Beyoncé 2," or "Little Beyoncé."

You don't mind the baby being named after your child... except that the baby will thus be given the same name as your child. My headache is worse. Must get off the Internet now.

thats how I ended up not being named Kimberly. that's my oldest cousins name so it'd awkward to have 2 first cousins (25 years apart might I add) named Kimberly

This is a silly thing to be upset about

My mother’s best friend named her second kid the same as my younger sister. They’re a few years apart, she swears she didn’t learn if the name from my mom. It’s a rather uncommon name.

TBH, it's not really any of your business.