Somewhere on here I read someone say that they wouldn't give out any of their personal ID info and I agree with that also. If I knew the child I would put on their my first name or something the child could identify with but family couldn't trace. I the child knows and likes you, depending on the child's age, they'll remember you and very well may try to find you. If you're making quilt for a child you don't know you could put a the date on it or some clue that will help them remember where and when it was given to them. Unfortunately in this time of volatile people, we do also have to protect ourselves and privacy.
By all means, make the quilt with all the love you can put into it and yes, please do put the child's entire name on the quilt large enough so there will be no mistake as to whom the quilt belongs. That's the best you can do.
Hugs,
Patty