This is probably one of the most obscure and puzzling names of any literary work I know of. As with anything else, research online will give us a basic explanation, but in my view this in itself doesn't totally account for why Mamet used the word as the title of his play (and film).

In the story, there is a confrontation between a college professor, John, and one of his female students, Carol. She comes to him after class one day, asking for help on an assignment. John immediately begins talking down to her, or rather, talking at her, deliberately using terms most students wouldn't understand and generally giving the impression that he has no time for her and that he's amused by her inability to grasp what he's talking about. Her frustration with him just eggs him on to continue in the same vein, lording it over her and reveling in this power dynamic of teacher-student and male-female. When she later brings harassment charges against him, he's stunned, supposedly not understanding that he's done anything wrong.

As one can see from online lookups, in its original usage "Oleanna" was a Norwegian folk-song about an ideal community in the US where immigrants from Europe were settling. The folk-singer Pete Seeger much later translated it and made it into a song naming a series of faraway, semi-mythic places where a traveler finds himself.

Mamet's use of the name probably has multiple implications. First, it suggests that the academic environment, which here is a microcosm of male-female relationships, is just as bizarre in its way as these distant and even alien places named in the song. Or, conversely, the otherworldly settings are an ideal one wishes to create or to escape to as an alternative to the dysfunctional setting of his play. The title seems to have an evocative power all by itself even if one does not know exactly what it means. The lack of obvious meaning almost enhances, paradoxically, our sense of the story's power, because the action of the play, though true to life, points out the absurdity behind such situations in the academic and the business worlds in which people (mostly men) can use their power to put down or humiliate their "underlings." These demonstrations of power are incomprehensible in some way, and it takes a stretch of the imagination to figure them out, to understand the real reason they occur. The unrecognizable term Oleanna is itself a metaphor of the incomprehension with which we're confronted.

This question invites interpretation by audience members, as only David Mamet, the playwright, can answer the question with certainty.

Mamet may have titled the play "Oleanna" to emphasize the theme of failure, as the title alludes to the failure of Ole Bull, a Norwegian settler who unsuccessfully sought to establish a utopian society in Pennsylvania in the 1800s.

Higher education has long been an element of the American dream, and students from all backgrounds attend college or university as a way to further their educations. This kind of academic pursuit of intellectual ideals is under examination in the play "Oleanna" and both the student and the professor experience a kind of failure of communication. "Oleanna" address the power dynamics between professor and student as well as the power dynamics between a man and a woman; in both contexts, the failure to communicate reveals cracks in the academic system and in wider society.

"Oleanna" does not directly refer to the broken dreams of Ole Bull, but it does allude to the failure of American society, whose male and female members often fail to communicate properly.

Oleanna was one of four regions of 19th Century Pennsylvania settled by Norwegians hoping to farm the land, which turned out to be ill-suited for that purpose, while establishing a utopian society where all would live in harmony.  Inspired by the region of Oleanna’s founder, Ole Bull, a violinist, whose mother, Ana, provided the second part of the town name when combined with Ole’s name (Ole-Anna, Oleanna), an unidentified Norwegian songwriter penned lyrics satirizing Ole Bull’s vision of a planned farming community, which floundered due to the unsuitable geographical features of the land in question.  The lyrics were later translated into English and recorded in a song by Pete Seeger, which reads as follows:

Oh to be in Oleanna,
That's where I'd like to be
Than to be in Norway
And bear the chains of slavery.

Little roasted piggies
Rush around the city streets
Inquiring so politely
If a slice of ham you'd like to eat.

Beer as sweet as Muncheners
Springs from the ground and flows away
The cows all like to milk themselves
And the hens lay eggs ten times a day.

Mamet probably chose the title “Oleanna” because one of the play’s two characters, the college professor John, similarly sees his vision of a utopian existence in the form of a pending real estate purchase disintegrate under the weight of his accuser, Carol’s, allegation of sexual misconduct.  That Mamet was inspired by the history of Ole Bull’s vision for Oleanna and by Seeger’s version of the song was evident in the playwright’s use of lyrics from the song at the end of an early draft of the play.