Unlike Mother and Father, Younger Brother's name doesn't immediately scream "symbol alert!" Unless "Younger Brother" has somehow become synonymous with "antisocial compulsive bizarre-o behavior" and we just didn't get the memo.
First off in the long list of Younger Brother's weirdnesses is the fact that he confuses love with obsession, focusing his desire on Evelyn Nesbit because of her famed beauty. He's so "desperate to have her" (1.2) that, like those stalkers that chase after actresses today, he is convinced that Evelyn needs him.
The only difference is that, because this is before the days of paparazzi and TV (and background checks) Evelyn actually goes out with him. She realizes, however, that he's not so much in love with her as a person as he is with her image. She also realizes that he's a strange guy who likes to hide in closets and pleasure himself. Evelyn gives Younger Brother the good old "It's not you, it's me" speech and Younger Brother is broken.
When the idea of idealizing a woman doesn't work out, Younger Brother moves on to idealizing a cause. He takes on the anarchist ideas of Emma Goldman, and pursues them by joining up with Coalhouse's gang. He later joins up with revolutionaries in Mexico.
Each time he adopts the identity of the people he's fighting with, whether by shaving his head and putting on blackface (cringe) or wearing the bandito dress of the Zapatistas and being "accepted as a compañero" (40.3).
So while Mother's Younger Brother's name doesn't announce its symbolism with spotlights and a megaphone like "Mother" or "Father" do, the name's symbolism is still very much there. Younger Brother is a sad dude who finds his identity in relation to other people: Evelyn, Coalhouse, and Pancho Villa. So it's fitting that his name itself shows his relation to, well, his relations. He's not himself alone; he's Mother's Younger Brother.