Too close?

Back Story: We have been looking at the name Gemma since our first daughter was born (it was the runner up and I only ever told two people) and still love this name. We’re thinking Gemma Grace (with the possible nickname G.G.)

A couple days ago my husbands cousin who is due early May announced her babies gender and name: Emma Kristine. Now I don’t know if they’ve just always planned on announcing everything at once or if she is subtly staking her claim. I’m due at the end of March and announced we are having a girl but I don’t plan on announcing name until after birth. Are Gemma and Emma too close? Would she think I’d stolen her name? Advice? I don’t know... This baby has been so much more stressful and this is just one more thing I’m worrying about. Am I overthinking it?