Is this other person the father of your baby?
If you intend to stay living on your own with your child then i'd advise from putting another persons name on the lease,this to me says that they are living there as well. Why would anyone want to be added to a lease when they wont be living in the property. It's going to raise a lot of questions, when your baby is born and you claim lone parents they might want to see a copy of your lease agreement...how do you explain that you have someone else on there because you are worried about coping on your own...it doesn't make any sense. If this other person was claiming benefits as well and on your lease they would see this as you living together and you would have to claim together.
The babys father is allowed to visit you and your child, and as a new first time mum if you had someone helping you for the first few months i dont see that they could hold that against you. Just be honest with them and dont try to hide anything. If your not together with the father then you have nothing to hide.
And as for coping alone with a new born baby.. i know it seems like it's going to be impossible but your'll get into a routine and you will manage. Everyone feels that way when your near your due date.
I was 18 when my first child was born and i was on my own also and bricking it on how i was going to look after this little baby all by myself. Have you been in contact with your local health nurse i found mine a great help. If you have worries you could arrange for her to come and see you when you arrive home from the hospital to help you settle in.
Also get in contact with your local CIC you can ask them all the questions in the world and it can be easier than speaking to the social welfare,