Yep, her name is simply "Mother." That's got to have resulted in a lot of playground taunting.
It's also a clue (with a flashing neon arrow sign that says "This is a clue!" pointing at it) that Mother is a seriously representational character. Mother represents the changing viewpoints of women as they gain more personal, psychological and even sexual freedom at the turn of the century.
In the beginning of the novel she respects her husband and thinks of herself as little more than a mother and wife, whose main job is to take care of the needs of others. After all, her husband is an important man, and she couldn't possibly survive without his strength and his business know-how. She's just a weak, feeble woman. But then, all this changes.
The single thing that affects Mother the most is Father's voyage to the Arctic. During his absence, Mother takes over the family business and sees it for the "dreary unimaginative thing it was" (33.4). This causes her to lose respect for Father, and increases her confidence. Turns out, Father ain't such a genius… or could it be that Mother is actually one smart cookie? Whatever the reason, Mother really comes into her own.
Not only does learning the family business affect Mother, but so do the events of Sarah, the baby and Coalhouse. It's Mother who installs Sarah and the baby in their home, Mother who keeps them there even after Father returns, and Mother who understands Coalhouse's pride and the importance of him and Sarah making a family.
Basically, her attitude towards Coalhouse & Co is representational of her own situation. She's a woman, and so is used to being treated like a second-class citizen, much like Coalhouse is used to being treated like a second-class citizen because of his race. Totally unfair on both counts. Ugh, the past sucked.
But she admires a) Coalhouse's pride and b) his dedication and determination towards his family. Since we're dealing with a character called Mother, we're guessing her actions are going to be about as transparent as her name. So her allegiance with Coalhouse shows that she also has pride and dedication towards her fam.
She also, as it turns out, has a pretty healthy sex drive.
Mother doesn't like anything about sex in the beginning of the novel, though she allows Father his time with her once a week. It's robotic (and not in a hot way, you weirdos). Later on, once she has gained confidence in both business and personal affairs, and once she's learned to assert herself, we see Mother beginning to notice her own sexuality. Bow chicka bow bow.
She also notices men noticing her, and begins to see the lack of imagination and soul in her husband, demonstrating "his limits, that he had reached them, and that he would never move beyond them" (33.4). Tack the phrase "in bed" onto the end of that statement, much like you would with a fortune cookie fortune.
Mother's growing confidence and ease with herself are matched by Tateh, who she marries a year after Father dies on the Lusitania. For Mother the book has a happy ending, as she takes care of all three children (Little Girl, Little Boy, and Sarah's little boy) in California after marrying Tateh.
Ta-da! Even though Coalhouse can't live happily ever after with his combination of pride and family values, Mother can.