We have not yet had the kids' mikveh (Jewish ritual bath) or given them Hebrew names. If they'd been born to us, they'd be considered Jewish from birth, and they'd have received their names shortly thereafter. But, because we adopted them, we have to give them names now. (Note: This ritual is only the beginning of the conversion process. If the kids wish to complete it, they will do so in their teens by agreeing to become bar and bat mitzvah.)
Our rabbi isn't concerned that we haven't done these things yet. However, I'd like to get on with them. The kids have been asking questions like, "Mom? What's Dash and Violet's Hebrew names?" Further, K will need to know her Hebrew name next year when she begins religious school.
We expect that the mikveh will be fun and easy, since there's a beautiful, progressive facility a few towns away and the kids love water. I've both experienced and witnessed the ritual, which entails a thorough scrubbing beforehand in a bath and then immersing three times in the ceremonial pool. I think the only difficulties will be scheduling it and getting the kids out of the pool afterwards.
So the complicated part is figuring out what our kids' Hebrew names ought to be. M and K's American first names are their Russian first names; then they each have two middle names. One of these memorializes a beloved relative; the other is my last name. Their own last name they share with Peter. Yes, that's right: Peter and the kids have one last name and I have another. We gave each kid my last name as a middle name because we'd read that adopted kids, especially older ones, worry about the commitment of the family member not "on the team."
So--we have passed on some family names in English and passed on both last names while still keeping the Russian names. We hope M and K will feel a loving combination of claimed and respected when they understand our reasons. But the Hebrew names? What to do about those? Our rabbi suggests we let them be"son of" and "daughter of" Peter and me, not of Abraham and Sarah, the way adult converts are named. But we're still hashing out the rest. Should we name them for more relatives? How about honoring their birthparents somehow? Their caregiver Mama A? We're still working on the problem.