Well, the key to good product placement and identification is to have a name that associates a purpose or process.
Since this clever device will probably at least in part be marketed to the knife guys, why not stay with that theme? Since it opener of bottles (like a nail nick opens a knife), and is excellent for opening cans (thereby saving a nail or three) like a nail nick, how about "nail nick" or some variant to get the ball rolling?
After all, it looks like you could use the can tab opener (not kidding here) on some of those GEC nail breakers that are out there by the hundreds, and anything else like that you didn't want to break a nail on. It looks like it would work well on some of the tinned spices I buy like my Coleman't mustard that requires I go to the garage for a screwdriver to pry the metal pressed lid up. This could work as a tiny prying device to open small cans of paint, the cocoa powder in the pantry, and on an on. Anything that looks like you should be able to pry open with your fingernail, but it is just a little to hard to do so.
If it was marketed outside the knife world, I still think "The Nail Nick" would be catchy enough to work and still get the message across, and no doubt future users or your device would find their own uses for it if the name was inviting enough for them to look at product. Using a name that associated it with beer, a bottle or can opener, or a swat team would probably limit the appeal of the product.
If I was going for folks outside of the knife and tool market (say marketing it as a handy tool for a lady friend) I wouldn't use a name too macho that would shut out your female audience (like "beer nut", "it's about the size of a nut but can open any beer, so get one for your beer nut"), or an acronym that only those "in the know" would understand.
Robert