I think overall it was a li’l bit of iTunes, Amy, Hasbro, random complainers, and perhaps some other reasons for why they had to censor the Derpster. Overall, I guess we should be glad she’s still in the show at all. (Remember back when we used to think she was gone for good?)
 
Ironically, nobody ever complained about the freaky “April Derp” clone in the current TMNT show, (which even says “derp derp!”) and that never got censored, as far as I know.

@Background Pony #7374  
But no matter how many complaints there were, 15, 20. We can be sure that almost none of them were from parents. Parents do not care about the name Derpy. Parents do not care about the word derp. Parents simply could not give less of a shit about this, which you could not say about the butthurt emanating from tumblr when Derpy got her own speaking role. The butthurt due to Hasbro catering to bronies.

@Background Pony #AC18  
…
 
Let me repeat those quotes from Amy Keating Rogers’s email:

(emphasis mine)
 
Note where she says “Positive and negative feedback was also being sent to Hasbro and the Hub.” So, yeah, I don’t see this as supporting the claim that there were only 10 complaints, period.
 
As for the video you linked: Yes, I do believe that iTunes was the primary reason the episode got (badly) edited; however, when someone who works on the comics says that there were no complaints, and someone who has worked on the show since the beginning and wrote the episode in question says there were some complaints, I’m going to have to say that the person working on the show is more likely to know what actually happened.
 
(Personally, if AKR got about 10 complaints, I’d say that the total number of complaints was probably fewer than 30, and almost certainly fewer than 50; however, that’s just informed speculation.)

@Background Pony #AC18  
F*ckin iTunes.

@Background Pony #7374  
That’s what Amy Keating said as already mentioned over and over again.
 
Oh you know what, screw this. Here is the cause. Now we can stop blaming parents. Yay. Right? Right?!

@Background Pony #7374  
Unless we have access to Amy Keaton Rogers’ email, as well as the other show’s staff’s, and/or Hasbro’s/HUB’s email, we’ll never know exactly how many it was…

@Background Pony #AC18  
And your source for there being only 10 people complaining about “Derpy”?

@Background Pony #7374  
Occam’s fucking Razor. The only people you ever see complaining about Derpy’s name online are social justice warriors. Never do they say they’re a parent.

@Beau Skunky  
What I meant was I like the name “Ditzy-Doo,” and it used to be almost as common a fan-name for her as “Derpy” was, but after the “Derpygate” fiasco, fans started hating it, and/or any of her other alternate names, (only other one I can think of was “Bubbles,” which wasn’t as common as “Derpy,” or “Ditzy”) so that kinda created a mess of things.
 
Sense they’re apparently not allowed to use “Derpy” anymore, and because they don’t want to upset fans further, they just leave her nameless now in the show, and merch’. So I guess she can be called whatever you want. Even “Steve” if you want.
 
Honestly, I don’t care if they gave her an official name, even if it isn’t “Derpy,” or “Ditzy.”

@Background Pony #7374  
@Background Pony #6920  
Some fans did call her “Ditzy-Doo” prior to the whole “Derpygate mess,” because of what Faust about considering making Derpy her, as a callback to the Winter Wrap-Up ep’, but as she said, people can still call her “Derpy” if they like.
 
I don’t get why people get so bent over either name, I call her both “Ditzy,” and “Derpy” personally, but obviously “Ditzy Doo” kinda fell out of favor, after the whole “Derpygate” fiasco. So now fans insist it’s either “Derpy, or nothing.”  
…Hence, why they don’t name her at all in the merch’ now.
 
Call her “Derpy,” people freak, call her “Ditzy” people freak… You can’t win.

@Background Pony #733B  
>When I first wrote this episode, the character under such harsh scrutiny was named Ditzy Doo. We had already established in previous episodes that she was clumsy (she is not the pony you want on your moving crew).

@Vree  
OK, I searched for Lauren’s Derpy/Ditzy comment; her exact words:

So I didn’t remember the phrasing correctly, and she may not have meant exactly what I said. Still, that is the origin of why some people call her Ditzy Doo.
 
As for those Derpy recolors in “Winter Wrap Up”, I’d need to see something from an animator saying they intended any of them to actually be Derpy. Because if that was the intention, why color the mane and tail differently?
 
(And I may be misinterpreting something here, but I don’t mean anything negative when saying fans who didn’t like the name Derpy “latched onto” the name Ditzy when Lauren Faust mentioned it. Here is the word of God giving them an alternative to a name they dislike, a name that furthermore might have become canon. Of course they’ll start using it. Personally, my preference would be for her actual name to be Bright Eyes, with both “Derpy Hooves” and “Ditzy Doo” as nicknames that, while initially intended to be unflattering, don’t faze her. Also, I remember the more rabid “Derpy Hooves” fans insulting anyone who preferred other names in the wake of Derpygate; it almost reached the point of making me swear off using “Derpy” ever again.)

@Background Pony #AC18  
From Amy Keating Rogers’s email about Derpygate: “I got about 10 emails saying how offended folks were. […] But I was not the only one getting contacted regarding Derpy’s portrayal. Positive and negative feedback was also being sent to Hasbro and the Hub.” (see /2012/02/amy-keating-rogers-response-to-derpy.html at the Equestria Daily website, or do a search for her response yourself)
 
So yes, I’d like to see your source that it was “10 social justice warriors” with absolutely zero parents. (And that’s a sincere request. If there’s any information about Derpygate I’ve missed, I want to know about it, in case it proves useful for future kerfuffles.)

@Background Pony #733B  
She didn’t have a design back when Lauren first she commented that she might give the name to DH’s palette in WWU;  
but the episode when it aired did end up featuring Derpy (although with purple hair and normal eyes, but the same color and cutie mark), in the role of Ditzy Doo:  
 
(above: Ditzy Doo leading home the Southern birds during the happy ending of WWU, after things gets re-organized by Twilight)
 
Note that DH’s crossed eyes only become adopted on the show later, and BG pony consistency didn’t exist until s3 and before color palette and cutie mark swaps and bg clones were very commonplace.  
Winter Wrap-Up is a perfect example; Derpy herself swaps mane color several times in the same one episode:  
 
But some bg artist clearly intended it to be her.
 
The name “Derpy” did not enter canon until the Last Round-Up, and Derpygate only made it worse cause fans of the name “latched onto” it (your words, @Background Pony #7374 :p) and bullied everyone still using the name Ditzy into submission by accusing them of supporting cenzorship.

@Background Pony #7374  
They said exactly what happened. 10 social justice warriors caused this.

@Background Pony #733B  
Because before “Winter Wrap-Up” aired, Lauren Faust said that a “featherbrained” pony named Ditzy Doo was mentioned but not shown, and speculated that the staff might use that name for Derpy. Fans who didn’t like the name Derpy Hooves (yes, they exist, and even existed back then) latched onto that.
 
@Background Pony #AC18  
Absence of evidence is not evidence of absence. Especially when the people who actually know what went on had to be very careful in what they said, and were soon forbidden from saying anything, a restriction that I think is still in place.

@Background Pony #733B  
They also never said any parents ever complained about Derpy, but that hasn’t stopped people from claiming they did.

Why do people continue to insist that Derpy’s name is “Ditzy Doo” ? I mean, ffs, Faust herself said that Ditzy Doo never had a design.