...are the two most precious materials in Rapture named ADAM and EVE? Surely, if there wasn't any religion of Gods in Rapture, they wouldn't name those after biblical figures. Why are they named like that?

It's a celebration of the power of man, since Adam and Eve were human.

Because Charles Darwin fucked a monkey.

While Ryan based the society on those principles, you found a lot of people in the world connected to religion in one way or another despite this, so the names could have been a sort of expression of that supposedly repressed need for religious mythology in things. 

It could have also been satirical by the developers of Adam and Eve, talking about how combining EVE energy and ADAM-based modifications are the source of a new humankind, much like Adam and Eve are the source of the Hebrew people in the Bible.

No Gods or Kings does not mean no history or symbolism. The day Wednesday is still named after the god Odin but we can know that, not believe in Odin and not think it is worth changing it's name at the same time.

"Rapture"

owned

Remember Andrew Ryan was an extreme atheist, going so far as to outlaw the bible (hence why the smugglers have crates of bibles) even in his non-state society. The city was named Rapture as a joke, rapture is were all the sinners will be left when judgment days comes as well as meaning a feeling of sublime bliss (sin and joy go hand in hand). Now why the Doctor named the products Adam and EVE i'm not sure, perhaps she also enjoys the same atheist joke as ryan or perhaps she feels those words best present how powerful these substances are, but from a thematic standpoint rapture is very much a place of decadence and decay and thus twisting rapture in something beautiful yet deadly and making Adam and EVE sources of life, power, death, addiction and madness is a good reflection of the state of Rapture, a city of beauty which has decayed and degenerated into something violent and destructive.