fighting with my boyfriend about our baby girls nMe

We finally found out the sec of our baby through our gender reveal. It's a baby girl. Just what he wanted...  I'm surprised because I was expecting to have a boy. I didn't have a preference. Since we found out of our pregnancy, we decided to choose names. We knew it was going to be hard to find the perfect name. If it was a girl he definitely wanted her initials to be GEM. His mothers middle initial is Elizabeth. A beautiful name, so I didn't mind it. And she had to have a G in her name to go well with her initials. We decided on Grace Elizabeth.... now he likes Gia Elizabeth. I don't like it. It's not fair he gets to choose the initials.... the name.... and what is had to start with. What sounds better ... Gia Elizabeth or Grace Elizabeth