I have several baby hostas for trade. They are green with a light yellow rim. I do not know the name, I could add a picture if nec , looking for other hosta to trade. LMK.

By babies, do you mean they are seedlings? If so, they are hybrids and don't have a name other than one you might give them. But it is rare to get a variegated seedling. If they are seedlings, how old are they? A hosta can change dramatically in characteristics as it matures.

I have had the hosta for a few years, each year they produce more babies (small plants) by multiplying. Have too many of the same one. Would like more of a variety.

Iraley, what zone are you in? When we bought this house we had some green Hostas out front and I divided them each year till I ended up with 36 huge Hostas and I gave them all away except for the babies I planted under the trees. The babies would pop up here and there and I would did them up. I also decided I wanted a variety. Do you have any pictures of your babies and how about the Mother plants.

By the way to the Hosta Forum, hope you will stick around and learn about different hostas like me, I now have about 100 different ones and ViolaAnn is great inspiration, she has a huge garden and great pictures.
Check out the link at the bottom of her post and see the sights.