Liseuse.
I don't know what to call it. I have a PRS-505, and Sony obviously spent absolutely ZERO time considering marketing and branding, because "I love my PRS-505" does not exactly roll off the tongue. (It's officially a Sony Reader. Yeah, there's another fine useless term.)
People ask me if it's a Kindle, and I say, "no, it's the competition." And then they ask what kind it is, and I say "Sony, only this one's obsolete; they don't make this version anymore."
I mostly default to calling it my "ebook reader," which is clunky. I may start using "ereader," even though I have fond memories of the ereader file format; it doesn't look like B&N is protecting their trademark for the name, so "ereader" may become the public term for the devices.