Baby Surprise was the baby that came with a cloth pouch that you put in the water so that the cloth would dissolve. Enclosed was the baby's 'papers' and its name, which you would mail into the company so that the baby would be registered to you. Until you put the doll into water you wouldn't know if the baby was a boy or a girl - that was the surprise! The little paper booklet that came with Baby Surprise included several ideas for names for your new baby.
There were also similar toys Puppy Surprise, and Kitty Surprise.