There are two ways to insure a surrogate driver if your own license is suspended. The first is for your surrogate to purchase their own policy. The policy would have to satisfy the mandates set down by the DMV, but can be attached to your vehicle. The policy has to be in the other driver's name, but will fully cover them and satisfy any legal parameters. This step may require your driver's name to be on the title as well. The best thing to do is check with the local DMV to find out specifics. The other way is to add them to your already existing policy.
Many insurance policies can have more than one primary driver. Mostly, this is to accommodate married couples how share the same vehicle. The policy would be under you name but would cover the other driver. This is nice because the other driver does not have to sign up their own policy. It also eliminates hassle if the arrangement is not a permanent one. Every insurance provider is different in what they allow and restrict. The best thing to do is contact a representative and find out if they even allow this option first.