I would guess that the article in question refers only to episodes within the story of Abram/Abraham between the leaving of Ur and the birth of Ishael. It is early in the story of the institution of the ritual of circumcision (Genesis 17) that his name is changed to Abraham. So, are all the biblical references to Genesis chapter 16 or earlier? If so, the use of Abram is correct. But anything with a reference later than Genesis 17:5 needs the form Abraham. When writing about the character himself rather than simply recounting the story, however, it is more usual to refer to him as Abraham.
Interestingly, however, Jacob who also has a name change (he becomes Israel from the time of his encounter with the mysterious person at the Jabbok ford) but he continues to be referred to as Jacob and only rarely as Israel.