Regal was a trade name used by Wulschner and Son, a music company founded by German immigrant Emil Wulschner in the early 1890s in Indianapolis, Indiana. Around 1896, Wulschner began manufacturing Guitars and Mandolins carrying the Regal plus other brand names. In 1904, after an economic downturn, the Regal name and Wulschner's remaining stock were sold to Lyon & Healy. A new Regal company started in Chicago in 1908 and it is supposed that they were tied to Lyon & Healy but at some point they became a separate company again and L&H transferred the registration to them in 1924. 

From the outset of the new Regal, they were apparently producing Ukuleles, (though I've never seen any pre 1920). In 1930 Regal bought the bankrupt J R Stewart factories and brands, (so the L & H factories but not the L & H Brands which were owned by Tonk Bros. but Regal went on and made most of their Ukuleles for them). They inherited the JR Stewart original names like "Le  Domino" and had their own brand name too. Like the other manufacturers of the time Regal Ukuleles were "endorsed" by the stars of the day, with some like Wendell Hall having their own signature models including the Red Head - Hall had red hair. (Hall also had a deal with Ludwig for Banjos).

 A great deal of their output was OEM for the big US distributors to re-brand and sell, so there are a lot of Regal instruments that have brand names from other companies and its experience that tells us it was made by Regal, (even with experience you will see a lot of probably by Regal as a lot of the Chicago manufacture was very similar and staff learned at one factory, then took their building techniques to another when they changed jobs). Then there was joint ventures like, in 1930 Regal, Harmony and Globe got together and produced the Vacationer Range - 12 Colourfully patterned low end Ukuleles, 4 patterns from each company and they shared the advertising bill. Another collaboration brand was Collegian and this one I have seen used in conjunction with distributor brand names so Tonk sold Washburn Collegian and B&J sold SS Stewart Collegian 

In 1934 Regal brought Dobro and moved manufacture from California to their factory in Chicago, (though apparently Regal had been doing the wood working for some time previous to this, and after the takeover Regal still brought the resonators from John Dopyera who was now running National again; so not a lot of difference).

In 1928 Regal invented a new instrument they called the Octophone. I believe it started out as a Mandola but some bright spark at Regal decided it could be tuned to be any of the chordophones so marketed it as 8 instrument in one! These was suppose to be a Ukulele, Taropatch, Tiple, Mandolin, Mandola, Mandocello, Tenor Guitar and/or Tenor Banjo and was one of the precursor instruments to the Baritone scale

During the Second World War Instrument manufacturing lines were converted to the war effort and although production resumed after the war it was never that great. In 1954 the factories and brand names were sold to Harmony who did use the brand names, with a changed logo that just said Regal in black letters, on a number of instruments. They then sold the name on in the late 50's to Fender who did sell some guitars with the Regal name at the time.

In 1987 Saga Musical Instruments, a big US distributor acquired the Regal brand name from Fender to put on imported Resonator Instruments, (using the old green logo to hark back to the days when Regal owned Dubro), including Ukuleles, (from some time after 2000). It also distributes budget Ukuleles, (with the later "Harmony introduced script" logo on, plus "Made in China"), and a number of other Ukulele Brands in the US

Regal also can partly be dated by the headstock logo used as it changed over the years but it's trickier than some because they also used a number of special headstock logos or sometimes didn't use a logo at all. I don't have dates for the changes but in a rough chronology: The Earliest don't have a headstock logo, (though this happened on some later models too?) - Then some time in the 1920's came the circular black label - next some time in the late 20 or 30's came the green label with the crown protruding through the top of the oval, this lasted certainly to WWII - after the war the label was more blue and the crown was inside the oval - finally there was just the lettering and this, I believe, started when Harmony took over Regal. (If anyone knows better please let me know?)