* Vertical Word Puzzle: This is a general term that describes any puzzle where words are arranged vertically.
* Downward Word Chain: This highlights the sequential nature of creating phrases from the vertical word.
* Word Ladder: This term is often used for puzzles where you transform one word into another by changing one letter at a time, but it can also be applied to this scenario.
* Word Mashup: This term emphasizes the mixing and blending of letters and syllables to create new words and phrases.
Ultimately, you can call it whatever you want, as long as it clearly describes the activity. If you're looking for a more creative name, you could even come up with your own!