If it’s a regular standard (non overdrive) transmission, it would be Ford’s own design. The transmission would have a rectangular side cover, secured with 9 bolts. In later Ford parts books they referred to it as a L/D or light duty type and also you could see a reference to it as a 2-15/16” type……this refers to the centerline spacing between the input shaft and the counter shaft.
In the replacement gear aftermarket (led by Borg Warner) they referred to the 1951-62 versions of this type as the 259 series. For example, the part number for a 1951 cluster gear was WT259-8…….. the main drive gear was WT259-16…..and so on. Of course there were many variations of the gears through the 1951-62 types, depending on the tooth counts and other differences.