What is the meaning behind Re-l's name? In one episode we see Re-l's name on a computer terminal. However where the "-" is, we see it's actually supposed to be an "A" as the rest of the letter is just visible. This means her name may have been supposed to be Real.

I am wondering: if there is some sort of meaning behind Re-l's name having originally been Real but being recognised as Re-l?
Her name is written in katakana as リル・メイヤ (Riru Meiya), leaves her romanized name up to interpretation... but it's speculated that there seems to be a some parallel between the her ID number (124C41+) and the episode title: リル124C41+/RE-l124c41+ and Re-L as a character. The code is based off of a sci-fi novel by Hugo Gernsback, titled Ralph 124C 41+. The title in itself, is a play on words meaning "one to foresee for one another (1 2 4C 4 1 +)".

It's assumed that the significance of her name is based on the protagonist of the book, who saves the heroine by directing energy at an avalanche, and then continues to do on about about modern technology and the wonders which actually proved as successful predictions in regards of the technology we have today. E.g., solar power, transcontinental air travel, synthetic foods, tape recorders, etc.

I assume that like most (if not all) of the characters in the series, she's named after historical figures, philosophers, and/or fictional characters. 

There's speculation in the fan community that Re-L may be an imperfect clone of Monad Proxy and her name is a reflection on that.