One of the things that bugs me about Moll Flanders is who she does and doesn't give a full name to. Significant individuals in her life, such as Jemy or Humphrey, get actual names, which makes sense given that they are, as I said, significant individuals to her. Jemy was her last husband, and someone who understands her a fundamental level (he comes from her world and speaks her language, as it were). Humphrey was her son who cared for her in her waning years, and was the first biological family member she truly accepted into her life.
But then we have the brothers she grew up with: Robin and the Elder Brother. She was madly in love with the Elder Brother. He was her first love and she had all her hopes and dreams set on him. And yet somehow he is just "the Elder Brother". Then we have Robin, a young man who loved her dearly, and towards whom she felt no great affection whatsoever, and ultimately held no great implications to her life and development. But he gets to have an actual name assigned to him.
But given the defictionalization of narratives in the time period, it's possible that maybe it was done to protect the reputations of the extant. Robin died, thus didn't need his name protected, so he could get his name. But the old nurse who took Moll in as a young girl is also dead, but gets at best an inconsistent naming convention. This was the woman tantamount to Moll's mother and Moll couldn't even be bothered to give her a real name.
The most likely reason I can find for why Moll is so disjointed in nomenclature stems from the fact that she is in her hinter years and just doesn't remember their names anymore. And from a real world perspective, it's possible with the onset of dementia or Alzheimer's, but from a craft sense, that's such a boring reason for Defoe to intentionally create an ambiguity of reference in the narration.