Most renters insurance companies will sell you a renters insurance policy whether you're on the lease or not.
So in most cases you do not need to be on the lease or have a lease to get renters insurance.
Renters insurance is sometimes required by landlords and only costs around $10.00 to $20.00 per month which is well worth it.
It's better to have the renters insurance and not need it than not have renters insurance and need it.
The renters insurance will cover the cost of any damage to your property such as if there was a flood, fire, mold etc and your personal property in the building gets damaged.
If you have roommates and they are not on the renters insurance policy that's okay as well because your roommates will still have their personal property covered under your own renters insurance policy if you allow them too.
So there's no need to buy more than one renters insurance policy if you don't want too.