Q. Is there a special name to be given to a child who was born with severe birth defects and not expected to survive?

A. Bris Avos (8: 4) quoting Chida mentions that there is a minhag to give to the severely defected children the names that are also used to name animals, such as Tzvi, Arye, or Rochel, as a segulah to their refuah.
However, minhogim differ and one should follow the traditions of his community.
Horav Shlomo Miller’s Shlit’a opinion is that in this case, since the baby born is severely defective, the tefilos prayed on his behalf, should mention that Hashem in His great mercy should do whatever in His infinite wisdom is best for the child.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a