I don't understand why you guys all think the overspend is the powerful part of the card. It *can't* be. I mean, if it's just a weak card to have, you're almost never going to buy it. At 3, you've bought a weak card - not good. At 4, you've replaced a card from your deck (not even the worst, but a random; you do get to keep it if it's good, but then you've just done exactly what you'd do at 3, which was weak for 3) with a weak card - not good for 4. At 5, you've gotten rid of 2 cards and gained a weak one - REALLY weak for 5. And it's just basically never worth it until you're at like 20 and somehow didn't have buys and need trashing even though you managed to get a ton of money already. So if the play effect is bad, it's just a bad card.
Fortunately, I don't think the play effect is bad. I'll admit that at first I missed the 'name a card' and thought it just trashed any duplicates in the top 3 cards. I'm actually not sure which one of those is stronger, I guess probably this way is, but whatever. I think this is a pretty strong early trasher. The nice point is that it clears your deck out while still giving you a 4 card hand to buy some piece on this turn, which is a pretty huge boon compared to the likes of something like chapel. On the other hand, it's probably a little slower - I have to imagine that most of the time, you're hitting 2 cards - and it has some downside. And like chapel, it's pretty dead later in the game (well, this can re-order the top three cards of your deck, which, say it with me, is almostabout half as good as a scout terminal scout). where does this put it? Well, it's hard to say. Probably, this is worse than ambassador and steward for me, roughly on the level of chapel and remake. Hrm, probably objectively a hair below them.
Other notes: one of the key weaknesses here is that it can't trash cards in your hand, so it does not do so well at keeping an engine deck clean as almost any other trasher. It will thin you and get you going faster than most anything else, but it just has very bad staying power especially in the face of junking.
It does quite poorly against ruins, as you have to name the right one.
It gobs up rats, true, but how often will you have both?
Opening math:
Let's say you open with this on $5, turn 1. Well, presumably you will trash both cards that pop up. There's a 30% chance of hitting estate-estate, after which you're in GREAT shape. There's a 60% chance of getting estate-copper, which puts you in pretty good shape (probably). And there's a 10% chance of hitting copper-copper, after which things look pretty bad indeed. Then T2, you have whatever 3 cards you didn't trash, plus a copper and either another copper (2/3 chance) or the doctor (1/3 chance). The problem you might have here is just getting the doctor with estates. Well, more on that in a second, but while this spread of options is good, you have to ask whether it's better than opening with whatever premium 5 is on the board? Sometimes, I expect yes, but random guess I would say 60% of the time, no.
Actually, let's say you opened Nothing/doctor-for-3 (okay, you never do this, but I am making a point here). What card are you going to name when it comes around? If you draw it with 3 estates, I assume you name copper and trash three, your doctor will come around soon enough, you ought to be able to chow estates, and you can start building some 3s up. If you draw it with no estates, very easy, name estate, and you are in amazingly good shape. With one estate, again you probably name estate even though there are more coppers left in your deck. Hmm, this one is close, and probably good either way. But the worst is if you get it with 2 estates. You can't buy anything, if you name copper, you ensure you'll draw that next estate, and you might trash yourself down to copper and 3 estate and doctor (reasonably high chance of this), which is really not somewhere I think you want to be. Now, I assume that having the other card you normally will is going to make this a lot more palatable, but it's a consideration.