Terrible idea. There is a reason Presidents and Presidential candidate don't name potential nominees before they are nominated. First, an enormous amount of time goes into vetting potential nominees, so as to avoid (or hopefully avoid, at least) any embarrassment or scandal. Second, and more importantly, putting a sitting judge on an official, public short list for a higher judicial office compromises the judge's neutrality (or perceived neutrality, at least). Anyone who comes out at the losing end of a decision made by the judge (especially in a criminal case) will argue on appeal that the judge's decision was influenced by his desire to stay on Trump's short list. And, before that point, many litigants would argue that the judge should recuse himself for the same reason.
Publicly releasing a list like this risks creating a YUGE mess. And risks effectively ending the judicial career of anyone on the list.
Not so.
There are judges sitting there right now who rule based on a potential pick for a higher bench. That is nothing new.
There is no reason, other than politics, to hide potential nominees to the Supreme Court.