Python comes from Monty Python. C++ is the successor of C. C is the letter after B (another programming language). Haskell is named after Haskell Curry. Ada is inspired by Ada Lovelace. Java is coffee. Lisp is a contrived abbreviation of LISt Processor.
All of these facts can be found on the Wikipedia pages for the languages listed above, and more or less all other programming languages in existence have similar information linked to them—even ML, the MetaLanguage.
But not Julia. 
Because there does not seem to be any reason: https://github.com/JuliaLang/julia/issues/5499.
“It just seemed like a pretty name”, referenced in the linked interview, is a reason—and an acceptable answer to me, if it is true.
I always assumed it was a reference to the Julia Set
And while we are discussing trivia, what is the reason for the weird hats at page 6 of https://github.com/stevengj/18S096-iap17/blob/master/lecture1/Course-overview.pdf?
[EDIT: fancy, not weird is the term I should have used. Thank you @Evizero.]
fancy hats need no context
Here’s a random thought, maybe only remotely related to this. Since the file extension for Julia source code is .jl, why not reinterpret those two letters to signify one of the defining features of Julia — JIT compiler on top of LLVM? 
Which refers to a video at Shows | Microsoft Learn. Stefan and Jeff answer the question at time stamp 18:54.
Really guys, you would make everyone’s lives so much easier if you just started telling people it was named after the Julia set 
I was really hoping it was named after “Julia” from 1984, but random name is still a good naming convention.
When I first heard of the language, I thought of Julia from 1984. Now I will always feel the language is named for that fictional character. So, to me, it is named for the 1984 character.
Now that this old thread has been resurrected, I feel I also have to leave here my (admittedly retconned) favourite semi-official explanation:
(As the preview cuts out the punchline, it is: "Jeff’s uncommon lisp is automated)
Welcome, @Jason_Smith, I believe this is still official from Wikipedia (I’m not sure why people don’t look up, by now, there):
in April 2012, Karpinski said of the name “Julia”: “There’s no good reason, really. It just seemed like a pretty name.”
Jeff is also a co-designer of Julia, and only in 2021 he wrote (that’s also quoted on Julia’s Wikipedia page):
Maybe julia stands for “Jeff’s uncommon lisp is automated”?
I feel like the latter is a joke, a fairly elaborate one (you have to know of the Lisp language, and maybe Jeff’s other language FemtoLisp, a Scheme/Lisp variant, which is actually also included in Julia for its parser), but you can’t state that on Wikipedia.
I at least feel the “Maybe” crucial, and “it is” to be avoided. I realized you used the word “reconned”, but I wasn’t sure how known that word is, not being a native speaker, so I checked. It’s from 2003 (or earlier), a comic book term (short for short for “retroactive + continuity” from 1983 book or earlier).
https://en.wiktionary.org/wiki/retcon
I did learn there’s yet another word stetcon, not yet in Wiktonary:
Julia can also mean “youthful”, a derivative of the Latin word “iuvenale”.
I think this is pretty fun, so I insert it here: (ChatGPT)
What? where did it get that from? Is that a version that has been lurking in the internet? Or is it just totally made up?
Discussing what ChatGPT spits out is — in my opinion — significantly less interesting than discussing dreams.
That is quite a philosophical question – it is from ChatGPT, so totally made up (based on Machine Learning) would fit quite well I think 
