What does Hana's middle initial stand for? In Hanayamata, Hana's full name is "Hana N. Fountainstand" (or Fontaine-Stand, or Fonteyn-Stand, or Founteyne-Stand, depending on who you talk to). Do we ever find out what "N" stands for?

I'm pretty sure this never happened in the anime, so I'm expecting it was revealed in the manga if it ever was.
It doesn't seem to be revealed anywhere officially, but based on fans' theory:
The "N" should be a word (that has similar pronunciation with) "Now".

Japanese fans found that all* characters in Hanayamata are related to Kamakura city in Kanagawa Prefecture, Japan.

From an anon user id 900RcZoqa on post no. 960 on 2channel,


  全部地名
  
  『ハナヤマタ』
  関谷なる → 鎌倉市関谷
  笹目ヤヤ → 鎌倉市笹目
  常盤マチ → 鎌倉市常盤
  西御門多美 → 鎌倉市西御門
  
  
  
  All of them are name of places
  
  "Hanayamata"
  Naru Sekiya → Kamakura city, Sekiya
  Yaya Sasame → Kamakura city, Sasame
  Machi Tokiwa → Kamakura city, Tokiwa
  Tami Nishimikado → Kamakura city, Nishimikado  


that leaves Hana N. Fountainstand.

Turns out there's also a place in Kamakura city called Imaizumidai. Imaizumidai in Japanese is 今泉台. If each character is translated to English,


今 = Now
泉 = Fountain
台 = Stand


they match with "N. Fountainstand".


  ハナ・N・フォンテーンスタンド → 鎌倉市今泉台（Now→今 fountain→泉 stand→台）


As for what does the "N" stand for, we can't really know, since as it's been mentioned, フォンテーンスタンド might be read as Fountainstand, Fontaine-Stand, Fonteyn-Stand, Founteyne-Stand, etc. Thus, the "N" might be Now, Nau, Naw, etc.



*Except Sachiko Yamanoshita. There's no Yama-no-shita in Kamakura city, but there's Yama-no-uchi and Saka-no-shita. (From Japanese Yahoo! Answers)

Also, there's someone who travelled around Kamakura to find these places. (1, 2)