I agree that this movie is tricky to rate. First, Wladyslaw's mother is credited as "Mother" in the credits and script. Since all of the characters refer to her as "Mama" or "Mother", I think this should count as an actual name. Sure, its not a "real" name like Halina or Regina, but its more of a name than, say, "Woman shot by Nazis."
That being said, while the family conversations sometimes make it difficult to whether someone is talking to a specific person or the group at large, I was able to find two instances of direct exchange between Halina and Mother about money.
1.
MOTHER: What on earth are you doing?
HALINA: There's a good place under the cupboard.
2.
HALINA: Mama, what is it?
MOTHER: Twenty zlotys. That's all we've got left. What can I buy with twenty zlotys?
Halina and Regina are mostly in the same scenes as each other, but they never talk to each other directly. Dorota and Janina never meet any other named woman.
Wladyslaw's mother is unnamed.