[Facts] Re: Last name options
Unless paternity has been established, the mother has the right to put "Unknown" on the child's birth certificate in place of where your last name would go.
Once paternity has been established (and, depending on which state in the U.S.A. you live in, this can be done as simply as your signing a paternity affidavit, or by the mother publishing your name in a newspaper) you will be financially responsible for the support of this child for perhaps the next 18 years of your life.
If you are not married to this woman who is about to bear your child, then you have a LOT of things to discuss with her. Perhaps the least important of all is the vanity of seeing your last name on the birth certificate.
-- Nanaea