We call her Derpy but what is her name officially?

Is it Muffins?

And did they refer to Derpy by name in the Slice of Life episode?

I need to know for a person I'm trying to help write with.

7742793
Either or. She's gone by both in the show but they changed it cause some harpies got themselves the vapors because little precious saw a pony their mothers deemed as "retarded" as opposed to just being a loveable clutz

7742793 This gives a good overview on the history of her name: https://mlp.fandom.com/wiki/Derpy

It seems like she's been named multiple things, even in merchandise or games or other products.

A common one that comes up in product advertising seems to be Ditsy Doo. But I think the fandom basically just calls her Derpy Muffins. She's unnamed in a lot of trading cards and merchant due up the controversy in The Last Roundup.

Maybe Derpy is a nickname, while Muffins is her real name.

I believe her official name is Muffins and Derpy is the fan name (she was given it after the first episode and even though the show staff made it "official" in "The Last Roundup", angry mommies forced a change). When she came back in Season 5 (I think), she was given a name "Muffins" and in merchandise she usually appears with a muffin symbol instead of a name.

I thought it was Dizzi Hooves or Derpy Hooves.
Maybe Derpy Muffins Hooves

yes

7742793
Muffins is what Hasbro uses, if that's the important point in your decision. In a fic, however, I'd usually expect her to be called Derpy. I wouldn't be especially startled to see Muffins, but it's definitely less common -- in part because the great days of Fimfiction were before the name "Muffins" was introduced anyway. Ditzy Doo is pretty unusual, though one or two popular authors do use it -- FanOfMostEverything is probably the most prominent of those.

Also, and I'm going off memory here so I stand to be corrected if I'm wrong, I'm pretty sure M. A. Larson said in an interview at some point that in the script he initially submitted for "Slice of Life" he used "Derpy" for her lines, but Hasbro insisted he change it to "Muffins" even though the name was never actually spoken in the episode.

7742793
My headcanon is that:
Muffins is her birthname (From her mother)
Ditzy Doo is her real name (Legal change at adulthood)
Derpy Hooves is her nickname (A name Ponyville gave her)

Ditzy is my favorite.

7743085
I don't think family names are really a concept that exists in Equestria.