Single Mom getting married, do I need to update my child's birth certificate with my new last name?

No you only change the child's birth certificate if your husband plans on legally adopting your child.

No cause the mothers madien name go on the birth certificate weather you are married or not

If you ever need to prove you are the baby's mother, you'd need to show something (like your marriage certificate) that shows you were previously known by the name that is on your baby's birth certificate. It really doesn't matter whether you were a single mother or not at the time; you'd have the same issue if you'd been married to the baby's father, got divorced, and were now remarrying. (This is just one among many reasons why I think the custom of having women change their names when they marry is silly.)

Unless your new husband plans to legally adopt the child. if the father is still in the picture expect him to be pissed if you do this

It's not necessary. Just make sure you keep your records in a safe place.

Thanks for your responses.