Bloodline Dons
Around the time of this movie coming out, and in some cases earlier, all the five families switched from a bloodline succession to new blood. By the mid seventies I don't think any of the families had a leader who carried the 'family' name.
So by the time gf3 was set it would have been unique for a Corleone to head the Corleone family. I only mention as a lot of posts speculate as to how Fredo etc would have got on.
Although it's worth pointing out that the mafia became increasingly weaker after this bloodline transition.
They say 'the Sopranos is very realistic and let's face it, they're only 1 cut above a set of street hoods.