Okay guys I've been stewing on this for a long time: what is Kay Faraday's name pun?
I'm probably missing the bigger picture but I had a pretty good idea initially and digging for information gave me a plausible answer.
As you may know, Ace attorney has a LOT of name puns and meanings. It's not wrong to dig into the importance of the characters name's, because it often brings a lot more meaning to the character.
So the biggest thing I want to mention is that Kay Faraday has a TON of motifs in their name and behavior that leads all back to thief motifs, and oddly enough, electrochemistry and and physics. And I say this with ELECTRICITY in bold because there really are a lot of connections.
Why?? I haven't the faintest idea. But I do have some theories. But first lemme explain the connections she has. So it may seem like a stretch at times but hear me out.
So first things first. FARADAY. This is the name of a British scientist who discovered the amount of electric charge (in Coulombs) in one mole of electrons. (For those of you unfamiliar with this terminology, Coulombs is a unit of energy and moles is a unit of mass). The name of this amount (in C/mole) is called Faradays's Constant. Faraday is most commonly associated with Faraday Cages, which prevents electrostatic and electromagnetic influences. Faraday is also know to be another word for wood. Now, there's a lot to unpack here, but I will come back to this later for interpretation because I need to discuss her first name as well.
Next is her first name, Kay. This one is harder to interpret considering Kay could mean a lot of things. Most significantly, we know Kay means Key or Keys in history and in several languages. And we also know that Kay has a "Key" motif as the Yatagarasu. There is also the possibility of her name meaning "Okay." However, there is one other connection to her name. There is a constant in physics that has a strong connection to Faradays's constant and electric forces. K (Kay), is otherwise know as Coulomb's constant, which tells us the force experienced by two unit charges at a distance of 1 m from each other. Yeah, that sounds like a lot of science-y nonsense and it kinda is because it's description is not very intuitive. But that's okay! Because it's important to know that units of Coulombs is meters/Farad. Farads are also a unit of energy named after, you guessed it, Faraday. So we know Coulomb's constant, K (in units of m/Farad), and Faraday's constant, F (in units of Coulombs/mole) are both related to one another and are both incredibly significant to electrophysics. Lastly, we know that keys are related to electricity as well, since Benjamin Franklin discovered it's nature using a "key" and kite. I mean, come on, even the word "kite" uses the letter k in it.
So what does this tell us? Well a lot, and nothing at all at the same time. Because interpretations can sometimes be such a stretch that we chase our way down a rabbit hole and search for connections in any way we can.
But from all this meaning, there is a LOT to cover. So here's every interpretation I could come up with.
1) We know Kay Faraday at the very least could mean "wooden key," which would make sense because her Yatagarasu key had a wooden handle. But also it connects to her "Thief" motif and the fact that she "unlocks" secrets like a key to a wooden door.
2) Alternatively, it could also represent a key opening a "cage" (as referring to Faraday cages).
3) Speaking of Faraday cages, there is also meaning in an actual Faraday Cage's function. Since Faraday cages protects from electric influences, it could be a metaphor for protecting something from outside influences.
4) "Cage" also has a meaning that could represent being trapped by something. Considering she has the title of a "thief" which are usually put in "jailcells/cages," it make sense.
5) Since her name is Kay, it could also mean she's trapped by a key. (Hence the name, "key cage"). This would make sense considering she was "trapped" by her past, by the Yatagarasu key, and by never catching the true murderer of her father.
6) "Okay" could be mean that she's sure of herself and her identity, or it could be a front to her inner struggles.
7) The connections to electricity and it's relation to the physics of "attraction and repulsion" (aka, positive and negative charges) could be a metaphor for the law, the "good" side and the "bad" side, or even a metaphor for her identity.
8) Electricity could also have connections to her jumpy and excitable personality.
9) A key and a kite? I mean come on, she has a key motif in her name and the Yatagarasu key, and she has a flying motif with her Yatagarasu symbol being a raven and "flying" like a kite to steal the truth!
10) Her strong connections to electricity in general could explain her "electric" futuristic tech, "Little Theif," to find the truth.
And this all is just in her name! This doesn't even cover all the significance and metaphors regarding the things she experiences in game. Or her identity as a thief. Not to mention the incredible amount of symbolism in a "three-legged raven." For heaven's sake, it's ridiculous how much meaning there is to Kay Faraday.
She's a really well developed character and she seriously deserves a ton of love and appreciation.
Also, why so many connections to electricity? I still really don't know. Creator's inspiration? Or just pure coincidence? Whatever it is, it works!
I'm sure there's still some meaning in her name that I missed or haven't mentioned yet. I didn't even cover the fact that she's a thief "for-a-day" (which sounds a lot like Faraday). Man, there's a lot of puns and meaning in Ace attorney character names but I honestly feel like this one takes the cake.
Anyway, I had a lot of fun writing this and thinking about the connections, even if it is a stretch. I feel like there's really no wrong interpretation for anything. Besides, it's really cool to think about!