JETX said:
It will be much easier if you were to formally adopt the child as then he will have inherent rights (heirship, etc.). If you don't, then you will have to always review wills, insurance, etc. to make sure that he is included.
Having permanent CUSTODY is not the same thing as a formal adoption.
I will also add, that unless dad's parental rights were officially terminated (not just that dad gave up custody) then dad would always be able to challenge your custody later. In addition, without adoption, even if dad's rights were officially terminated, other relatives, even members of dad's family, could also challenge your custody later.
I understand that you don't want your daughter to lose her official status of being the child's mother. However...there are many important reasons to do an adoption, and only sentimental reasons not to do so.
Also, in case you are concerned about finances, your grandchild will retain his Social Security Survivor's benefits even if you adopt him.