1. xom coloring studio
2. xom colorize studio
3. xom colorization studio
Where I come from (central USA), coloring has several meanings; the first of which is what small children do with crayons, and the second is what people sometimes do to their hair, so I suggest you don't use #1.
Colorize is a verb, so #2 is not grammatically correct in English.
Your #3 is grammatically correct and, in my opinion, a good choice, assuming your clientele are English speakers.
BTW, the name of your shop will be a proper noun, so all words should be in capital letters: XOM Colorization Studio
Student or Learner