It's not a common term but apparently cross-dominance or mixed-handedness is what it's called.
But I am not native English speaker, so maybe people from UK or US may know more
Discussion
I feel that the Japanese word "cross-handedness" is also not a very widely used word. I can understand why words related to cross-handedness are not often used in English.
The Wikipedia article is short, so it may not be a common term. Now that I think about it, I remember that I started hearing it in Japanese a few years ago. Sorry for jumping to conclusions…