This isn't really a "liars and truthtellers" puzzle so let's get this part out of the way: Zheng is correct that only one student lies. It's Annette, whose statement about everyone belonging to exactly one club is false. Everyone else is reliable. Also, Annette is a Puzzle Club member.
If the names of the Puzzle Club members spell out a word as Quentin says, it must be a word where all the letters are different. Per Studs, an integer number of Puzzle Club members represents 60% of the membership, so the number of people in Puzzle Club/the length of the word must be a multiple of 5. A five-letter word like that is easy; a ten-letter word like that is tough. Apparently the only fifteen-letter word with all different letters is "UNCOPYRIGHTABLE." There's no way Puzzle Club has 20 or 25 members.
Per Orson, the Puzzle Club roster includes Ivonne, Zheng, Uma, and Studs. The word cannot be "UNCOPYRIGHTABLE," so there must be five or ten members. Per Jarls, there are at least two more members, so there must be 10 members. Also, per Xena, Rochelle is the tenth member. Also, per Kyle, Terry is the eighth member.
To recap, our letters are AIZUSRT, plus ME or OG, plus one other letter. And the T is in eighth position and the R is in tenth position.
Neil says that Annette says that Quentin is no longer a member of Board Game Club, which means Quentin IS a member. Per Ferguson, anyone (other than Ferguson) who is a member of Board Game Club is also a member of Tennis Club. Per Yan, Tennis Club is a front for Polyamory Club. So Quentin is a member of Polyamory Club, which means he is the student with two girlfriends—which means, per Hubble, that Quentin is the founder of Puzzle Club.
We now know that the names of the Puzzle Club members spell out a ten-letter word that starts with a Q. There's only one such word, but before we go look it up we can deduce some more things. For example, per Wendy, Orson is the founder of every club he belongs to. So he can't be a member of Puzzle Club, so, per Jarls, Majda and Eowyn are members (and Greta is not).
The word is Q******T*R, where the missing letters are AIZUSME. Per Orson, the substring "IZ" is in there. Probably the U is right after the Q. Apparently you are expected to figure out the rest for yourself: The word is QUIZMASTER.
That is not the answer to the puzzle, though! Read the beginning of each Puzzle Club member's yearbook quote, treating Majda's silence as a space, and you'll discover that LYLE CAVES.