An impeachment trial in the senate would presumably be run through the Senate Judiciary Committee (presiding judge John Roberts), unless there are constitutionally permitted process rule changes.
Senate Judiciary Chairman Lindsey Graham begins to get specific about what he will and will-not allow as part of the senate trial.   Graham notes the ‘hearsay rule’ will be applied to the House evidence within the article(s) as presented.  Additionally, Graham notes that anonymous witnesses (ie. “whistleblower”) will not be permitted.