Alvin D Keech and his brother Kelvin moved from Hawaii to San Francisco in or before 1915 to teach Ukulele, Kelvin had, in 1914 published "A Standard Method and Self-Instructor on the Ukulele" and the school was founded on the back of that, (the school also sold locally made Ukuleles branded as Keech brothers for a while too - I have seen it suggested that one or both of the brothers actually made them but this was not the case). It may or may not be true he taught some of the Hollywood stars of the time, it appears to be true that he came up with the term Banjolele, (though he spelt it Banjulele), and it is not true that he invented the instrument. Another SF resident called John A. Bolander patented a, what was to become known as the, Banjolele in 1916, (it is possible they could have known each other?). Kelvin went to fight in WWI and after the war became a jazz musician in Paris. Sometime around 1920 Alvin joined him and they toured the UK as well as France. In 1922 Alvin published a tutor book, this time in London. In 1924 they had to move to London due to the French Musicians Union embargo on Americans playing in Paris. They set up shop in Bond St. and received the patronage of the Prince of Wales, who brought a number of instrument from them to give as presents. Keech appears never to have had a factory or produced any instruments himself, but he put his name on a lot of Banjoleles and some Ukuleles distributed through J. E. Dallas. At some point after 1928 the brothers move back to the USA, (I have seen photos of US banjoleles that claim to be Keech made and are different from the European ones but I don't know if they are fake?). 

In Europe, manufacture of Keech Banjoleles and Ukuleles continued until at least 1935 but had ceased by 1939. The Banjoleles branded by Keech came as standard or long scale in a number of decoration designations denoted by the first character in the serial number stamped on the neck heel. The Banjo Ukuleles usually had at least one reference to the UK patent on them though what the patent was for is unsure, (it was granted in 1925 in the UK). I don't know what Alvin's deal with Dallas was but it must have been good for them to not only continue selling Alvin Keech branded Banjoleles long after they had the far better endorsement from George Formby, but also after Alvin had shafted them by using the same documents to patent the Banjolele in France and sell this patent to J. Thibouville-Lamy & Co. who then got Windsor to make a pretty much identical Banjolele for them to brand! This betrayal led to Dallas re-designing the standard model and changing the model number from A to C to differentiate them from the Jetel copies.

All of the Standard bracketless models have a facsimile of Alvin Keech's signature engraved on the rear resonator, but they were all made by Dallas, (or from the look of them Dallas had George Houghton make certainly the standard scale ones), there were a number of different model numbers  for the Keech banjoleles A then C for the soprano ones, B for the long scale ones and J for the very best, (I have seen a model L too). Finally the later bracketed models with a serial number starting with X were made in Germany. 

The Ukuleles, (and there were Keech branded Guitars too), on sale in Britain were certainly made in Germany or Bohemia. All the Ukuleles I have seen were Long Scale but appear to have come from different makers, (Albo made some, but it doesn't look like all of them?) so you get different fixed or floating bridges, archtops and flat tops Bridge pins and ties but no coherent model numbers. that I am aware of?