I just came from Office of Vital Stats with a corrected BC (gender and maiden name).
Next week I will go to a court to petition to modify the existing Paternity order.
Blimey, that was quick.
I called the hospital on Tuesday. They said they will check my application and birth records. Yesterday I called them again. They said they checked the docs and transferred the corrections to Office of Vital Stats. I went there today and exchanged the BC (btw it was free of charge).