Short answer: always better to know before you show up at the pier.
First, the OP's question left a lot open to interpretation. As someone who has checked in cruise passengers, anytime we have questions or concerns, we are trained to ask our supervisors for help. There are situations that we deal with daily, and then there are uncommon situations that we ask help on. With the OP's vague question, I don't know if it is a straightforward situation of a married woman traveling on her birth certificate, or something unusual that a typical check-in agent would request a supervisor's assistance.
If I was checking in a passenger whose name on the travel ID documents didn't match up, and it wasn't a simple explanation of married woman using her birth certificate (maiden name) and DL (married name), I would wonder what was going on.
Sometime a young person would have a birth certificate with the last name of the 'no longer in their life father'. This young person may have informally taken on the last name of the step-dad, but the legal name hasn't been changed - so the BC last name, and the name on the booking don't match up. In this situation I would need a supervisor's assistance.
As I said, the OP's question was vague, and when I think granddaughter, I think young person (although I know that grandkids can be any age). Maybe the OP will come back and give more details.