That's all the Chief Justice has, just like everybody else.

The Chief Justice is a manager, and to an extent a leader, but the Supremes don't take dictation from anybody. So ultimately, Roberts will be known by his own record. The court will be called by his name during his tenure, but that's mostly easy chronological shorthand. The Court's record is determined not by the Chief Justice, as a Presidential Administration's is determined by its President, but more by the cases brought to it by the people, and by which cases they choose to hear and which they choose to dismiss to the lower courts without comment. Those are group decisions.

The people are the source of all court cases; the people decide what the Court will rule on by the kinds of cases we decide are important enough to bring before them.

The responsibility is ultimately ours.

Another phenomenon among judges: Though it's possible to predict future behavior by past statements, once freed from the pressures of political influence, Supremes sometimes deliver unexpected decisions from the bench, especially when they have been on the bench for many years. The change is slow, but gradually the focus shifts even in their own minds from being appointed by (and beholden to) a particular political group to a more independent frame of mind. This doesn't mean a philosophical change, though that too is possible, but it means that what we think we see is not necessarily what we will ultimately get.