I would use the last name as given on the earliest document you have. If you later find an earlier document with a different name, then you can change it.
If church records do not exist, then you can use wills, land records, bills of sale, contracts, or what ever exists.
In many church records the name of the child is given as a first name only, without the surname expressly attached to the child’s name. In those cultures where the child takes the father’s name this in straight forward. But in cultures where surnames are more variable, this assumption does not always work. Later documents will determine what surname they actually used.