Not Married, Non U.S. Citizen

My question involves paternity law for the State of: indiana

I am an australian citizen and about to have a child to a US citizen. If in case I am not here can I still have my name
added to the birth certificate? Or can the child use my surname?

You need to talk to the mother about the choice of surname. If you're not present, or if she chooses to exclude you from the choice of name with your having no established paternity rights, the choice of name is hers. Should she pick a surname other than yours and should it become necessary to litigate to establish paternity, you can try to get a name change, perhaps a hyphenated surname, by asking for that relief as part of your paternity action.

Do i have to be in the states to be added to thebirth certificate

If you are submitting an acknowledgment of paternity form in cooperation with the mother, I expect that the state will accept a foreign notarization of your signature line. Mom, if in the U.S., would need to have her signature separately notarized. The standard form anticipates that you would sign in front of the same notary, but it shouldn't be particularly difficult to adapt.