I just had a possibly bright moment (this occurs sparsely): Eevee probably comes from ‘EV’, the acronym of Exposure Value. But please correct me if I’m wrong. 
Maybe everyone but me had already figured this out, but I thought to post it anyway. 
It’s named after a pokemon character …
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My wife still plays the Pokémon mobile game every day. 
Extra Easy Virtual Environment Engine
Still, I’m sure it’s a wink to Exposure Value. I don’t believe it’s coincidental that ‘EV’ is pronounced as ‘Eevee’ and is a well-known photography acronym.
To me, it looks looks like EVE with motion blur. 
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I mean, it would make sense if Eevee was a colour management system, but it’s a little bit more than that. I would assume the most likely case is that the developers wanted to call it “Easy Virtual Environment Engine” and then just put “Extra” at the start so it is easy to say the acronym.
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No seriously. It is actually named after the pokemon:
https://twitter.com/tonroosendaal/status/809474433903722496
They made up the acronym after the project was called eevee.
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Exposure Value is about light intensity. Light is the most important property of a renderer. I think it makes sense, but the evidence is piling up that it’s just a funny coincidence, unless this was a hidden riddle by Ton, and the one who guessed it will get a free copy of Blender. 
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Oh god do I wish it was something as clever as that, but no as sozap said…
I’ve got to get me one of those!
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I always though blender name was related to blend modes or something related to computer graphics , but it was named because of a song by yello… devs are having fun with names 
At least Nintendo hasn’t yet sent a lawyer to the BF regarding the Eevee name.
Maybe they aren’t as protective of their IP in that area as opposed to someone making a fangame.
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They certainly may at some point (like after the final release is officially announced), but that’s entirely Ton’s headache if it happens. Worst case is likely that we all have to get used to a new name. So I wouldn’t be using the Pokemon character in the documentation or anything but otherwise it’s not really worth worrying about at this point I think.
Apple once had a product that was code-named Sagan. Carl Sagan complained they didn’t have his permission to use his name in this way, so Apple changed the code name to BHA. When he found out that stood for Butt-Head Astronomer, he sued Apple (and lost).
http://www.lettersofnote.com/2012/03/butt-head-astronomer.html
But if Nintendo feels they need to complain in order to protect their Intellectual Property then pretty much everyone will have to be all “Ok, sir, yes sir, we will change the name, please don’t destroy us.”
There could have been an argument (without the mascot thing) that the name would not confuse anyone because it’s the name of a computer program, not a cartoon character, but then Nintendo started making software titles with Eevee in the name so that argument is likely out the window.
And even if one were totally in the right, it’s all about who can pay for the scariest lawyers and absolutely the Blender Foundation has better things to spend our money on 
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I do agree that is a possibility, considering when dealing with a character owned by one of the most litigious companies in existence. The BF should have a backup name and logo for Eevee so they can swap if they need to.
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I always thought Blender was named after a certain kitchen utility.