When your guests respond, they will be able to RSVP for themselves. They will also be able to add a guest(s) and enter their name(s). This is what your guests would see after they RSVP "yes":
If you don't want your guests to be able to add additional guests, you can disable this from the Invitation Options page. You can also set the number of additional guests recipients can bring on the same page.
If you needed to manually add an additional guest for one of your recipients, try using the Connect feature which you can read more about .