Inherited tennant (and a second unbeknownst to me)

[Garrett Penfield]

Hi all, I recently bought my first duplex and inherited a tenant. I am living in the other half (unlike the first owner) and when I presented my tenant with a new lease agreement she immediately asked if she could add a person. I said sure they just need to fill out a form so I can do background and credit checks. I got it back and they left a large portion of it blank with the explanation "I'm still going to be responsible for the full lease, so Abbi didn't fill out the income part, and her lease history is the same as mine." She already signed a nine month lease and paid her deposit and first months rent on time. Something seems very fishy, but I'm not sure what it is. Is there any danger in having someone live there and not formally added them to the lease? Thanks in advance!