Same name

Okay ladies, this is really starting to bother me. Ever since I was about 15 weeks my boyfriend and I decided on the name Jase for our baby boy. We already bought the wooden letters for his nursery and told our parents his name. I'm now 29 weeks. In November my cousin, who I barely see had his baby and named him Jace! I don't want to change my babies name, and I'm not going to, but do you think I'm wrong? I asked one of my aunts her opinion and she said we don't socialize with that part of the family enough to let it bother me. Chances are I won't even meet the baby. I just feel like he's gonna think I copied the name. What are your opinions?