Doesn't get much more mythic than that, folks.

Hee. That is indeed an amusing game.

May want a clause "that no other player has named this way". Alternatively, may be just as fun without.

Why the nonlegendary restriction? Might as well go all the way over the top.

Holdover from before the "Not named this way" clause; preventing "Legend!" "Same legend, legend rule, pop. Hah!" loops.

Sadly, this card can be ruined by fuddy-duddys that insist on calling Angel of Despair, then targeting this enchantment with the come into play ability. You can't even respond to that. You'd also have to watch for players that would use this card to deal 7 damage to you, by immediately naming Karrthus, Tyrant of Jund. If players weren't that rude, though, it could be a lot of fun.

Make it indestructible and put the creatures out tapped.

Ick. Balancing's no fun.

EDIT: New idea: "At the beginning of each player's upkeep, they choose a creature not chosen this way with CMC X or less, where X is the number of ULTIMATE counters on ~. Then they put the chosen creature onto the battlefield and an ULTIMATE counter on ~."

This way, the creatures increase in cost and presumably power as the showdown continues.

Heh, that makes it even more Momir Basic-esque.

Well, it doesn't get rid of the Ronom Unicorn problem, but it's an interesting solution to the Gaea's Revenge problem.

Oh yes, that's an interesting game. What's the most broken non-legendary creature? Is there one that can outrace your opponent's new creatures?

­Drake Familiar is the obvious go-to pick. You can replay it next turn, but then they can name Drake Familiar again since the source is a new object (and even if it wasn't, they could just take Quicksilver Gargantuan of Drake Familiar, Clone of Drake Familiar, and so on). All that does is give your opponent a bunch of free stuff. (Kederekt Leviathan is also a possibility, but multiples of that won't stick around, and your opponent is more likely to be able to replay a blocker for it.)

Any implementation of this effect is basically going to hand the game to the first player who gets a use out of it , which is bad news if it's something you have to spend your resources to play in your main phase.

Oh! I'd never seen Drake Familiar, I didn't realise there was anything that could affect a specific permanent you didn't control without targeting it.

I'm not sure if this will ever be got to work as an enchantment, but I'm also curious which player wins if you take the rules as given and try to exploit them best.

It has to be something not answered by an opponent playing a creature copying it, or a creature killing it. I don't know if it's just a race for damage, or a race to see who runs out of creature copy/kill effects first, or if there's anything which if you get it down first will definitely let you win.

Possibilities:

One-hit-kill creatures, eg Blightsteel Colossus
"Can't lose" or "can't be attacked" creatures, eg. Blazing Archon
Creature-kill creatures
Creature-copy creatures
Raw damage race creatures

Obviously it depends what else you have, but there must be a best answer if you both started with 20 life and no permanents.

Are there any creatures which would make you lose (like Phage, but non-legendary?) It would be amusing if it was a deadlock and the players had to name every creature in magic until one of them named a losing creature :)

Alternatively, you could have all players name which creature they want at the same time. You could even make this card enchant a player and have the card trigger during their upkeep. That way, that player gets priority, and you could respond accordingly. The only real problem with this plan is that, instead of your opponent getting something super-broken, you're now the one responding to your opponent's super broken thing, and getting something that breaks your opponent. At least this way, though, the card operates in the broken way it was intended. ;)

Hm. In fact, "Gain control" creatures like Conquering Manticore may be very important. You can't start with a one-hit kill like Blightsteel Colossus because your opponent can win instantly with Conquering Manticore.

So you either need to name something which prevents your opponent getting more creatures, or exhaust the "gain control" effects first, and then go for kill cards.