Can other members on Family Sharing see when I add another family member?

Yes. Family Group members can see all the other member names. It is rather the point of sharing. Read Apple's support document What is Family Sharing?

If your unstated question is about concealing family members then you need to exclude these individuals from the group. Apple states also in this document that You can be a part of only one family at a time. This prevents the possibility of setting up two different family groups if you wish to have members separated.