Born out of Wedlock?

Coraleigh
I'm sixteen and currently almost 21 weeks pregnant. Me and my boyfriend, who is almost nineteen, have been together almost 2 years, none of this was planned. Me and him both had so many goals that we going to try and help push each other to achieve together. But I guess life has another plan for us, and we're going to try to do the best we can. His mom is super excited to have another baby in the family. She's buying stuff left and right. But she's trying to pressure me into marrying him so I don't have to put born in wedlock on the baby's birth certificate. She doesn't know why she thinks it's a bad thing, but she thinks it's a horrible thing and we should prevent doing it if we can. 
Don't get me wrong, I would love to marry him one day. And he wants to marry me, but he wants to marry me when I'm ready. I wanna finish school first and start the career I've chosen. I know having a baby before those things isn't easy either, but I have faith I can do it with his help. 
But are there consequences to having born in wedlock on a birth certificate? I even have it on my own.