First off, her name is not written as "kacheriina", it's "kacherina", so already the spelling that you've provided is incorrect for the name.
Secondly, I already provided an example of the letters "katerina" being spelled as "kacherina". The fact that there's another letter before them (Yekaterina being spelled as Ekacherina in Japanese) does not change that fact.
So no, it does not have to have been written as "katerina" or "katorina". There is already a precedent available that shows it can be written that way.
And, incidentally, when I google Kachelina it produces LAST names. Isn't "Kacherina" her FIRST name?