Triumph is one of the LK Links-selectable brand names in the CPC BIOS, allowing to display the boot message Triumph 64K Microcomputer on power up. Amstrad apparently planned a partnership with a company with that name. Which company this could have been is a riddle.
Triumph Internation Underwear is possibly the most popular company that uses Triumph as brand name. It is rather doubtworthy that Amstrad seriously planned this partnership.
Triumph Motor Car
Triumph Spitfire Mk II
Triumph Motorcycle
Triumph Bicycle
Triumph Records
Triumph Records
Triumph Typewriter
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The Triumph brand name is also used by several bicycle, motorcycle, and automobile manufacturers. Unlikely that Amstrad planned partnerships here, too.
There has been a typewriter manufacturer named Triumph, concerning the CPCs typewriter keyboard, this could have been a reasonable partnership - but that company was renamed to Adler long ago, so for that partnership, the boot message should have been Adler 64K Microcompter. Actually, the typewriter relation isn't too unlikely. The brand name Triumph-Adler (TA) has been used to produce various computer hardware from 1971 up to today.
There was also a Triumph Records company. Triumph is also a canadian hard rock band. There is also an Triumph Electronics company in USA, though according to their About Us page, Triumph Electronics incorporated in 2007 (thus it can't have anything to do with the CPC), interstingly, they say We stand out from the crowd by our professionalism (though as by 2010, the About Us page still doesn't work yet with Opera, nor mainstream browsers like Firefox or Internet Explorer).
See http://en.wikipedia.org/wiki/Triumph for more possible meanings.