She said that for the purpose of good storytelling. I don't know if you've seen Terminator 2, but if you have, you'll notice that just before Arnie often repeats lines, particularly "Hasta la vista, baby." This doesn't mean he is talking to a baby, nor does i mean who he is talking to is his parent, nor does it mean he is Spanish or has Spanish ancestry. It is simply a character repeating a line for effect. This is the same reason that Nora repeats the line "Mum's are tough", Snow and others repeat the line "The army's no match for NORA!", in FFVII Barret repeats the line "There ain't no getting off this train", etc. etc. etc. You repeat something because it defines your attitude, it reminds people of things, because it emphasises a point, because it is good storytelling.
This is nothing new. This is just defining Nora's attitude: A tough Mum. Every time she does something brave, she says the line "Mum's are tough."
Finally: People remember faces far more than names. If he remembered her name - even if vaguely... then he would remember her face - even if vaguely. But he never said anything about it being his mother, he said "your mother" to Hope.
I'm sorry, FE, but you haven't got the required evidence for this one, either. You can have your opinion on things and I'm sure it's very fun to make up little stories like this, but in the long run it serves little purpose but to satisfy your craving for everything to tie together on levels that are above and beyond the actual story.