The name Eden (עֵדֶן) also has the same root as the Hebrew word for "gentle" (עָדִין). In Hebrew it is pronounced EHden, Eh as in Esther, and it can be both a boy's or a girl's name.
The Hebrew term may derive from the Sumerian "EDIN", which means "steppe, plain, desert, wilderness". The Sumerians used the term to refer to lands west of the Euphrates.Another theory is that it comes from a Semitic root word meaning "abundant, lush".
I have heard that "Eden" means "delight" in Hebrew. I don't know if this information is valid though. It is my daughter's name and she is truly a delight.