opinions please

I'm really just asking how other women feel. Do no be rude or judgy because I will ignore you so quick. 
I am 14 weeks and will not know the sex of my baby for another two weeks. However, my guy and I have been shooting around both girl and boy names. The first name we agreed on for a girl was rose as a middle name (which I LOVE). It wasn't until about 2 weeks after we agreed on it that I realized that his most serious ex-girlfriend's middle name is also rose. Could that be why he agreed.. I don't know, it's also in his family (namely, his little sister). I immediately told him, no way we are not doing that because she's insane. However, as time goes on I'm really wondering if it's even that serious.. do you think it would be that big of a deal if we did name our little girl ____ rose???? (I have a first name too, just don't want to disclose it yet). The ex lives thousands of miles away and they have not been together for almost two years now. He's over her and does not speak with her. She, however, tries very hard to find ways to come back into his life.