My wife and I (no known Jewish heritage) are adopting an infant child. The child's birth-mother was herself adopted and raised as a Jew by Jewish parents. We do not know of any Jewish heritage through the birth-mother's biological parents.
I have heard that rabbinical authorities will recognize people as Jews under certain criteria and that one of those is Hebrew naming. Other answers to similar questions I have found indicate that a child of a Jewish mother is automatically considered a Jew, but in the case of our child, that seems to beg the question. In our case, it seems that for our child to be considered Jewish, it would have to suffice for either the biological or the adoptive mother to be Jewish.
Basically what I want to know is, is there something I should be doing now that would give our child the ability to be recognized as Jewish later in life if desired (for example, to qualify for the right of return to Israel)? Or is that basically impossible in our situation? Are there some authorities that might recognize our child as a Jew and others that would not?