No, not really much of an issue at all. I never changed my name when I got married, so didn't see any reason to change it when I had a child, though we did give our son my husband's last name. My son has never asked why my last name is different, he grew up with that reality and so had nothing to compare it to, and he knew all my family has my last name (my parents, etc.) so the name was around. Your child will probably assume for the first many years that each person gets his or her own name and that is that, and might only ask about it later.
Ok so really not that big of an issuse, that i cant live with
My last name is different from that of my son, and I do find it a little bit of an issue now that he is in grade school. The school has never questioned me about it but sometimes I feel like his little pals and their mothers think I'm not my son's mommy because they know my name is "Smith" and he is "Jones." I've even found that occasionally I'll mention something about when I was pregnant with him, to another mom, just so she will know I'm not my son's stepmother but his actual mother. It is not a major issue, but it arises every now and then. I wouldn't want my son to feel like it estranges us from each other or anything.
unisex first name (we both like)
husbands middle name
my last name
Jordan Chase Geary
Might be more of a hassle for travelling purposes if your child has a different last name on their passport than you or your partner.