One issue is that your former spouse is likely a second-named insured. This is normal for married couples, but typically less common for other types of relationships. You’ll need to confirm with your insurance company that your former spouse can be a named insured. If not, your insurance company may require a re-rating of your policy, which means your rate could change.
Another thing car insurance companies will look at is your address. If your former spouse no longer lives with you, most companies won’t allow them to be on a policy with you. You would each have to get separate policies for your vehicles at the addresses where you reside.