Pyrrha has too simple sounding of a meaning to me. Pandora of course is also within the trend of being named after a single person, but I want more than that to accompany the next treasure. Connecting Pyrrha with fire only makes it sound more centralized and simple to me, because then both that woman and fire are necessary details, specifications for people to disagree with. I don't see this sort of name as open.
Dragon is general, it has no connection to the Pandora (or successor) aside from ED's screen name and website. I like a lot of dragons, I like jagged furry flightless monsterbeasts more, but I wouldn't suggest the Pandora 2 be named after one of them simply because I like them, for the same reason that I don't endorse people calling it Dragon simply because they like dragons. We like the device too, right? Isn't it more respectable to name it something with some reference to itself, rather than that other cool thing you're into? Other thoughts, I can see there being confusion between a device called Dragonbox and ED's Dragonbox store which sells more things. And Dragonfly has nothing to do with this handheld at all, people just think it sounds cool, which is a nice plus but should never be the sole reason behind a name more serious than what to call your pokemon. I'll pretend I'm responding to everyone who has said only "I like Dragonfly/Dragon/Dragoon/Dracon, so let's use that," and ask, why? Where's the dragon in anything about this device?
Chimera turns me off because I'm most familiar with the meaning "created human," and I wouldn't like to think of this handheld as a human. It's certainly not just a turn off to me because of a friend of mine naming their character species "chimeras" despite it already being a more general name, and I'm so bored of his chimera porn. Not at all.
Hydra sounds related, the many heads to symbolize multitasking idea could go somewhere, and the creature is pretty cool and less overused than average. Sort of just makes me think of water right now though.
Pyragon, I don't remember the meaning/s suggested behind it, I think it's also mostly being pressed for sounding cool though so I'll talk about that. I don't like the way it sounds, I think of pyramids and Paragon Partition Manager. I really don't like the way it looks either, because of the Pyr. I have to think it's going after Pyro and Pyro is such a tiresomely used name to me. I see a Code Lyoko-headed cartoon child with a smiling determined face below bright gaudy flame hair, and their name is Pyro. I can see the Pandora idea's connection to Paragon, that's definitely there, but paragon's definition doesn't sound as fitting as myriad's to me.
Myriad is my favorite name for this handheld. It reaches far, infinitely far, but it does not force a connection with anything unfavorable or personalized. Open and infinite, but not infinite only to be unreachably long, infinite enough to allow smaller less beautifully precarious uses as well, perhaps 10,000 or so. Myriad.net is also available, if that helps.
I think Panoply is the right kind of idea, its meaning can be mirrored over what we like to aspire the Pandora's meaning to be. It's more specific than this usage in essence though. Also I um, don't like the way it sounds personally. Sorry.