The “Head PAD” (PAD(パット)長, Paddo-chō), or “PAD Chief”, was the derogatory nickname for the Touhou Project character, Sakuya Izayoi, as she is the 'head maid' (メイド長, Meido-chō)¹⁾ of Koumakan. It was a cheap joke that claims that she wore breast pads in Touhou Suimusou.

In the early 2000s, people were bound to compare how characters looked in the mainline games to how they looked in Touhou Suimusou, so people would joke that Sakuya Izayoi wore breast pads as an explanation. Obviously, we know that “Alphes” is not “ZUN” and that artistic liberties can exist, but this was during a time when cheap jokes were commonplace on bulletin boards, so people simply ran with the idea.

The joke's simplicity caused fan artists to use it as a cheap gag or signal 'breast envy' which could further the idea of 'femininity', then it became an overdone joke as people spammed it everywhere without reading the room (e.g. unprompted 'pad' comments). Eventually, the joke went away in the late 2000s as people were now propping up the 'rivalry' with Sanae when Touhou Seirensen released in 2009.

First off, we have the obvious antithesis of “Head of the Big Boobs” (巨乳長, Kyonyū-chō), or “Busty Chief”, to argue that her breasts are real, plus her more recent mainline appearances (e.g. Touhou Kouryuudou) would confirm that it was a skill issue. However, defending this interpretation without the latter context could easily get 'erotic' or 'sexual' as people generally love boobs and there's the maid uniform fetish.

After this, you have the synthesis of “Head Sarashi” (サラシ長, Sarashi-chō) which proposes that she binds her massive chest with sarashi in confrontational scenarios (i.e. the mainline games), but doesn't bind for casual scenarios as Touhou Suimusou was supposed to be casual banquet. Of course, an explanation like this isn't necessary and the theory sorta falls apart anyways.

Long after, there has also been the reinterpretation that Sakuya Izayoi does use breast pads in a semi-serious 'transgender woman' headcanon, as they wouldn't have the medical know-how or medicine until Eientei was integrated into Gensōkyō after the events of Touhou Eiyashou. There is also the addition that we know nothing about her life before Koumakan, and we've also seen what happened with Prince Shoutoku.

• Sakuya's title of 'kanzen de shousha' (完全で瀟洒), commonly translated as 'perfect and elegant', has opened up the door for potential 'PAD' backronyms in the English language. Such examples include 'perfect and dashing', 'perky and delectable', 'pointy and delicate', 'pillowy and defined', etc.
• On August 11, 2007, the Nae-Radi DNA Special before Comiket 72 with ZUN, the subject of Sakuya's breast size had actually came up, but ZUN ended up dodging the question.²⁾

• Meiling's Name

• Pad Chief on Pixiv Encyclopedia
• Pad Chief on Niconico Encyclopedia