What happens if I get a grant for my PhD project but I decide to quit and start another PhD somewhere else?
Of course you are not forced, nor obliged, to finish your current project.

But it might very well be that, depending on your grant conditions, you will have to pay back the grant money, fully or partially, when you do not finish the project.

Furthermore, it might be wise to try to keep being on good terms with your current professor and colleagues. This is most likely achieved by involving them in your decision and motivations (which you might already be doing, as you write in your question).