Baby Name "Stealing"

What would you do if you had announced your baby name and someone else used the exact same name as you? First AND middle. My cousin did this to me and now I feel like I have to change my baby name :( we didn't post it on Facebook, we kept it within the family, and my cousin was also pregnant and she posted it on Facebook! Didn't even tell us. When we asked them what name they liked it was completely different, and then they asked and we told them and this happened. I know no one necessarily owns a name, but they're close cousins so it'll be the exact same name. My feelings are really hurt and I don't know if I'm over reacting or not.