In rebuilding Japanese industry after WWII but for peaceful purposes, one avenue that was exploited was the manufacture of musical instruments, (Gakki apparently means musical Instrument in Japanese?).
Pre-War there had been a few well respected makers like Suzuki, so there was some skill available and it must have seemed like a safe idea - Until it killed Chicago, (and a lot of other US), manufacturing! Once in business, distributors found that giving the Ukuleles they produced Western Brand names was a better way to sell them, (somewhat similar to Chinese brands of today). Sometimes, with the older, long standing ones like T&D or B&J, they used old brand names they had used on Chicago made Ukuleles before the war and some like Westheimer just invented new brand names.
I have read that there were 80 firms started in Japan in the late 50's and early 60's to service the fretted chordophone boom but by 1970 50 of them had gone bankrupt! As far as I can see the same brand name may have been given to Ukuleles from a number of factories and each factory may have produced a number of brands, including some branded with their own Japanese name.
This post war production was primarily Sopranos and Baritones, (I've only seen a couple of Concerts and Tenors), and originally mainly from Japan, with a few examples coming from other countries in the region, but by the 1970s Japan was expensive so manufacture shifted to South Korea and Taiwan, (and eventually mainland China).
The Ukuleles themselves vary in quality from very low end to fairly high quality and some of these brands are now well respected internationally as makers. There are a lot of brands for which I have found very little information on apart from having seen some examples, some maybe "house" brands for the Factory, some would be for small distributors whose history now is gone; here is a list of brands I have found very little information on.
Alex-O (made in Taiwan) I have seen the headstock with and without the O
Altus (made in Taiwan)
Aragon
Asahi (Gakki)
Bentley
Blackstone
Blue Hawaii
Cameo
Capri
Castilla (Made in Taiwan)
Clear Sound
Coast
Crown Professional
Diastone
Daiichi (Gakki) distributed Ukuleles endorsed by Masao Koga, a famous Japanese composer
Dixon (Made in Taiwan)
Douglas
Empire
Exotica
Flamenco (Made in Korea)
Fortune
Hoffmann (nothing to do with modern Boat Paddle Ukuleles)
Jupiter (made in Taiwan)
Kahala
Kyomei may have made larger scales
La Valencia (Made in Taiwan)
Lero
Linco (Made in Taiwan)
Lunas Acoustic Works est. 1954 according to the headstock and made in Korea. They make acoustic Guitars as well and are on sale in Pakistan too, (so may still be in business?) They may also have a secondary Chinese made brand called Kahua?
Marathon
Marco Polo
Marlin (may still be branding budget instruments today?)
Masada
Melody
Minstral
Onken (Gakki)
Orlando
Pacific
Palmer (Made in Taiwan) Claims to be from Valencia, Spain on the sound hole label.
Prelude (Made in Taiwan by V.M.I.)
Regency
Rhythm Band Inc. est 1981 (made in Taiwan)
Robin
Shiro Musical Instruments They produced instruments branded Shiro, St. George and may have produce instruments branded Pleasant
Tara (made in Taiwan)
Tokyo Trading Co. They used the Romance brand name and a sound hole label saying "manufactured by Tokyo Trading Co"
Tomo (possibly made in Korea by a firm called Flight Mode?) There are some acoustic Concert Ukuleles with this branding and some twin pickup steel strung Ukuleles that have the branding Tomo Plug In Baby.
TGK (INA) (made in Nagato, Japan)
Venus
Windsor
York