My primary art is Danzan Ryu Jujitsu. This is a Japanese based system of jujitsu. However, Okazaki (the founder of the art) chose to use different, non-traditional names. For most Japanese based systems, Kote Gaeshi looks something like this:
If you ask a DZR guy, if we study Kote Gaeshi, he will say yes. But when he demonstrates it, it will look something like this: (Kote Gaeshi is done twice, once by each person, starting at 46 seconds in)
Note, they are completely different things. This leads to a little confusion when training with other Japanese systems, for obvious reasons. I bring this up, as you seem to trying to come up with some kind of key word, coding system for the techniques. My suggestion would be to use the TKD Korean terms. That way your TKD students will be compatible with other schools.
At first, it may sound like a way to keep your students from drifting over to other schools. But, it also keep other TKD students from drifting over to your school. Further, when TKD Grand Master WhatsHisFace comes out to teach a seminar to your students, you have to spend half the time translating your terms into his terms.
Using the common TKD terms for the techniques would be a better approach in the long run. Then you can call out the Korean term and they perform it. You can add modifiers, "left side forward, step back, TKD term," "left side forward, slide step, TKD term."