Baby’s last name

Okay, so for starters I’m in the state of KY- if that helps anything.

I’m currently 13w3d pregnant. The father of the child is involved, but there is only one issue- he’s still legally married.

I’m not sure if the divorce would go through before the child is born or not, but I’m just wondering something...

Since he’s still legally married, would there be an issue with giving our child his last name? 😬