Silent -
It's not Frank E, it's Frank P for Pentangeli. And they are not related. Pentangeli took over the Corelone operations in New York along with the Corleone compound in New York after the death of Clemenza. Obviously Frank P was under Clemenza and eventually was given the responsibility of running things in New York once Clemenza died. Now technically he was still part of the Corleone family( in business terms). Not a blood relative of Michael or the Corleones. Strictly family in the business sense. And being that he was still under the thumb of The Corleone Family, that is why Michael tells him that he is still part of The Coreleone Family and will continue to run the New York end like a member of The Corelone Family (business).
Hope that clears things up for you.
Don Cardi
