Transom

Cambridge Dictionary lists the bar first, labeled specialized architecture: “a horizontal bar of stone or wood across a window”, or a bar separating the top of a window or door from a small window above. That sense names a piece of the frame, not the glass on either side of it.

The second sense is labeled for American usage, with transom window as another name for it: “a small window over the top of a door.” That sense is the glass itself. Because Cambridge marks it as the American sense, it is the one that fits a homeowner in Naples pointing at the small window above a front door, and the bar sense can still describe the frame piece between that window and the door below it.

The National Glass Association never mentions transoms, but its exterior order places them: “Exterior cleaning should begin at the top of the building and continue to the lower levels to reduce the risk of leaving residue and cleaning solution on glass that has already been cleaned.” Applied to a single entry, that order puts the transom glass ahead of the door glass below it, to reduce the risk of residue landing on a pane already finished.

A transom's glass can be divided by a small grid, and the strips in that grid are muntins, which Merriam-Webster defines as strips separating panes of glass in a sash. Glass set in a high part of a wall, above head height rather than over a door, is described by a different word, clerestory. Glass on an upper floor raises the reach question answered at whether second-story windows can be cleaned from the ground.