Renters insurance, should the landlord be listed on the policy ?

[Kenneth Burke]

I have a new tenant moving  in, with two dogs (putbulls) I required her to obtain renters insurance for any injuries or damage caused by the pets. Should I be listed on the policy as well? And how do you verify that the policy covers injuries caused by the dogs? If there is any damage to the house caused by the dogs can I put a claim through the tenants policy? Thank you in advance for any guidance, information.