These unusual lanterns are confirmed to be made by SUGG, but an exact match cannot be found online. This leads me to believe that these are a bespoke design, unique (or at least designed for) Moor Street Railway Station - so they don't have an official name. I'm dubbing these the "Moor" lantern, with this page documenting the small version. They appear to have been created to run SON or MH lamps.

Birmingham

The small Moor lantern is installed in great numbers underneath the canopies of the platforms in Moor Street Railway Station.

Nowadays, these run LED cob lamps, but this suggests they ran SON or MH lamps once-upon-a-time.

A small number of these have (rather crudely) been adjusted to support Cameras. Personally, I'd have placed the camera inside the glass, and assigned extra cleaning to the glass of the lanterns.

This example is located on the corner, and is another example which has been modified to support a CCTV camera.

As well as the ceiling-mounted lanterns, several sets of column-mounted Moor lanterns are installed along each platform. The ones pictured below are on Platform 3.

These columns are original gas columns, and before the Moor lanterns, would've supported gas lanterns. Some of these columns on the far-side of the station are abandoned, and have four-sided heritage lanterns (converted for electric) which may be the last remaining of said gas lanterns.

A few of these lanterns are day-burning...

...But at least they aren't in this condition!

With the bowl loose, significant water ingress has caused premature lamp failure. It is technically day-burning, but the struggling lamp is too dim to have any-kind of effect on it's surroundings.

More Moor lanterns (play on words massively intended):