I'm not even a fan of Di, short form of Diana. But this is literally the English word for changing the color of something: hair dye, tie-dye, etc. And if you call someone this (even for Diana), it sounds like you're telling them to go die. Just my opinion.
I don't like this name. It sounds like the word for changing an object's color, and it looks too close to "die". It sounds like a nickname for Diana, not Dionisia. Besides, Dionisia isn't even an English name.
I don't think anyone would actually name their child this, but if they did, imagine if he was in a race or something. Everyone would be screaming "go dye!"... Haha.