On the End of Evangelion soundtrack, the artist is referred to as "ARIANNE".

Truth be told, the song bears a closer resemblance to a non-specific song by ABBA faithfully constrained to the chord progression (note singular) from Pachelbel's Canon than anything even remotely resembling "Hey Jude".

Additionally, I've played a concert band arrangement of a Bach piece called "Komm Süsser Tod", although whether or not this is simply a simplification in title of the Bach piece already mentioned above is unknown to me.

The following is the original poem penned by Anno, before it was "tweaked" into the haunting song from End of Evangelion. The lyrics we here in the movie/soundtrack are the interperetation of Mike WYZGOWSKI. They are extremely different from the literal interpretation of the poem, but in a decidedly pleasant/disturbing way. An original translation of Anno's poem can be found at http://avians.net/rkc/reichu/reichu-eva-csd.html (the English translation might be copyrighted or something, so it does not appear here):

"Amaki shi yo, kitare"

Fuan na no.
Fuan na no.
Minna ni kirawareru no ga, kowai.
Jibun ga kizutsuku no ga, kowai.
Demo, HITO o kizutsukeru no ga, motto kowai.
Demo, kizutsukete shimau.
Suki na HITO o kizutsukete shimau.
Dakara, HITO o suki ni naranai.
Dakara, jibun o kizutsukeru no.

Kirai dakara.
Dai~ KIRAI dakara.

Suki ni natte wa, ikenai no.
Dakara, jibun o kizutsukeru.

Yasashisa wa totemo zankoku Kokoro o yudanetara, watashi wa kowarete shimau
Kokoro ga fure-aeba, ano hito wa kizutsuku

Dakara, watashi wa kowareru shika nai
Mu e to kaeru shika nai

Mu e to kaerou
Mu e to kaerou
Sore wa, yasashisa ni michita tokoro
Soko wa, shinjitsu no itami no nai tokoro
Kokoro no yuragi no nai tokoro

Mu e to kaerou
Mu e to kaerou
Tanin no inai mu e to kaerou
Mu e to kaerou
Mu e to kaerou
Kizutsuku koto no nai mu e to kaerou...(REPEAT)

Run it through the babelfish. I dare ya!

If you don't want to bother following the link to find the translation, just imagine the entirety of Shinji's internal dialogue for one or two episodes formatted to look like a poem.

This is easily one of the most recognizable songs from any anime, anywhere (although "Sobakasu" from Ruroni Kenshin might be a good runner-up). It's catchy, it's eerie, and it takes place during an extremely disturbing and traumatic part of the movie. What more can you ask? It's a terrific song from when the vocals begin until the last minute-or-three, but definitely worth hearing regardless (just be prepared for gratuitous hand-clapping).

The only other time I've heard a woman sing so happily about suicide was "that Tori Amos song that my girlfriend always plays in her car that I can never remember the name of".