Most hospitals require a name on a birth certificate before you can leave, but you don't need to have a name before then.
Choosing a baby name can be very difficult! A name lasts for life, and no parent wants to hear, “I hate my name!” from an adult child later on. And of course, many families agonize over family names, while other families prefer traditional names or, alternatively, totally unique names. Sometimes the clock runs out, and you still haven’t decided on a name when the baby is actually born. Don’t worry! You do not have to have your baby’s name set in stone the moment you deliver; no newborn recognizes his or her name. That won’t happen for weeks after birth. However, you do have to have a name picked out for your new child before you leave the hospital as a name must be on the birth certificate.