A fan-shaped transom is known as a fanlight, especially in the British Isles.
From the en.wikipedia.org
There is a door on this level with a fanlight that provides easy access to the backyard.
From the washingtontimes.com
The door is surmounted by a large fanlight inside a projecting pediment.
From the en.wikipedia.org
It has a timber doorcase with a rectangular fanlight, a pulvinated frieze and a pediment.
From the en.wikipedia.org
The stone Doric doorcase has an open pediment and a radial bar fanlight.
From the en.wikipedia.org
The front doors are made of pine and topped by fanlight windows.
From the post-gazette.com
A leaded-glass fanlight and sidelights around the front door illuminate the main hall's grand staircase.
From the kentucky.com
The kitchen has several windows and a door with a fanlight.
From the washingtontimes.com
Above the doorway, a fanlight window directs natural light into the towering entry with marble floors.
From the latimes.com
More examples
Transom: a window above a door that is usually hinged to a horizontal crosspiece over the door
Skylight: a window in a roof to admit daylight
A semicircular window over a door or window; usually has sash bars like the ribs of a fan
A fanlight is a window, semicircular or semi-elliptical in shape, with glazing bars or tracery sets radiating out like an open fan, It is placed over another window or a doorway. and is sometimes hinged to a transom. The bars in the fixed glazed window spread out in the manner a sunburst. ...
A half-circle window over a door or window, with radiating bars. Also called circle top transom.
The glazed light above a door, often fan-shaped and ornamented - however the term is applied to any shape of light above a door.
A small window above a door or casement.
A fanlight is a fixed (non-opening), ornamental window of semicircular or segmental shape, typically found above the main entry door of Federal houses. ("Light" is a traditional synonym for "window.")
Glazed area above a door, if rectangular rather than semi-circular, semi-elliptical or segmental, more correctly an over-door light.