Triumph is one the LK-selectable Brand Names contained 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. Though it is rather doubtworthy that Amstrad seriously planned this partnership.
The Triumph brand name is also used by several bicycle, motorcycle, and automobile manufacturers. There was also a Triumph Records company. Triumph is also a canadian classic hard rock band. Unlikely that Amstrad planned partnerships here, too.
There has been a historic typewriter manufacturer named Triumph, concerning the CPCs typewriter keyboard, this could have been a reasonable partnership - but that company fusioned with Adler long time ago, so for that partnership, the boot message should have been Triumph-Adler 64K Microcompter. Actually, the typewriter relation isn't too unlikely. The brand name TA Triumph-Adler has been used to produce various computer hardware from 1971 up to today, spanning a range of electronic typewriters, Alphatronic PCs, and modern laser printers. More info on the company history is found on their webpage http://www.triumph-adler.de/ (german)
Note: According to http://en.wikipedia.org/wiki/Triumph_(TWN), the bicycle/motorcycle companies originally had the same source than the computer/typerwriter business.
There is also an Triumph Electronics company in USA, though according to their About Us page, Triumph Electronics incorporated in 2007 (thus it cannot have anything to do with the CPC).
See http://en.wikipedia.org/wiki/Triumph for more possible meanings.