You cannot change the birth notification name if the name was recorded at the hospital. This is because the hospital remains with a copy of what you took. However, if you took the birth notification without any names written on it and you wrote the name at home, then you can change it since the copy that remained in the hospital does not have any names.
If you have not decided on the child's name, it is advisable to not fill in any names on the birth notification. You can be given a birth notification without names and fill in the names later.