I don't have a name for them. they're usually a type of power gamer and on the surface they may appear as such. They are usually mechanically interested in the system and focused on combat effectiveness. One of my friends is my prototype for this player type.
In D&D they usually build fighters of some kind. Toughness is important. In post-Arcana 1st edition they built barbarians. Or half-ogres if that was allowed. Half-Ogre barbarians were probably their favorite. Swinging a two-hander in one hand with an 18/00 STR while having 20+ hp at first level was just the top of the world to them.
In Rifts they usually built Full Conversion Borgs and typically travelled with spare suits of Borg heavy combat armor- again, toughness is important. Railguns were awesome and their ideal character was the Red Borg in that one painting. The Germany Sourcebook was their favorite in those early days because it was full of awesome Borgs and some cool power armor.
In Champions they built bricks - Armor, Forcefield, Power Defense, Knockback Resistance, usually coupled with some kind of HTH Killing attack, often with armor piercing, typically in the form of claws or a sword. It's important to be tough and to look badass. Wolverine was probably their favorite character in Marvel, but Wolverine in Colossus' body was what they wanted to play.Haymakers and move through's were their main combat maneuver. No codes against killing here, friend.
In Gamma World they went for a mutant with Force Field, some kind of ranged attack, and enhanced PS or CN. If they didn't get something like that they dumped it and played a PSH, begging for Power Armor of any flavor, a vibroblade, and a nuclear weapon - hey they wouldn't stat them if they didn't want someone to use them.
In Twilight 2000 they took Recon 80 as a starting character. Always. They were also always Green Berets, Rangers, SEALs, Force Recon, SAS, or Spetanaz. They usually carried C4 in addition to at least 3 guns and an AT weapon of some kind - and they still moved like ninjas.
In Warhammer 40,000 he likes Terminator Marines, preferably Chaos Terminator Marines because they are more badass and all spiky and stuff. Lightning Claws rocked in Rogue Trader.
In Marvel Super Heroes they were Wolverine. Or Colossus. Or Thor. Or Thing if none of those were available and maybe Wonder Man if Thing was taken. At least he had shades.
I don't know what they play in DC Heroes - we never stuck with it long enough to find out. I suspect it would be Superman. Or, more likely, Darkseid.
In Traveller their goal is to talk the DM into staring with Battle Dress and a FGMP-15, but they will negotiate down to a PGMP-13 if that's the best they can get. "But the merchant can start with a _ship_" is a common refrain here. Failing that it becomes their #1 goal to get those things as soon as possible.
In Star Fleet Battles he likes the Klingon C8 Dreadnought because Klingons are badass and the C8 is an awesome ship and one of the toughest DN's in the game.
In Shadowrun they play the character with the .01 starting essence and were very excited when the cyberzombie rules came out in 3rd edition so they could finally break through the zero essence barrier. Humanity is irrelevant -being immune to Panther Cannon fire is awesome and having a reaction time so fast you can act before you even think of it is a great power.
So the defining thing here is to be tough, be able to kill things in cool ways, and to look awesome doing it. Now Paladins can do some of that but Paladins aren't cool to these guys - too many restrictions on behavior. Assassins though...
Anyway these are the surface characteristics of this player type. The real defining trait though
is best illustrated by an example from play:
Years ago I ran a Rifts campaign that lasted 15 months (no really I did). My prototypical friend was one of about 8 characters in the party on their long journey from Texas to the ruins of Detroit and back - this was my second campaign to feature PC nuclear weapon use). He was of course a full conversion Borg, straight out of the Germany Sourcebook, a Gold Borg I believe. They were finally at the outskirts of Detroit and had to pass through a graveyard to avoid being spotted by some bad guys. They encounter a normal looking human in the graveyard and ask him for directions - the guy blows them off. The Borg pops his fist-spikes, gets right up in his face, and threatens him. Said human picks up the Borg and throws him way over there wherupon the Borg, realizing he faces a vampire, hits Turbo Mode and runs right on back to camp at 100MPH. This is despite being maybe the least vulnerable character in the party to a vampire as he's mostly metal. Didn't matter- that thing might have hurt him, so he ran away.
This encounter was when it crystallized for me - the same thing had happened in several games before - he builds the toughest badass he can within the system mechanics of whatever game we're playing then proceeds to sit at the back of the party most of the time. When combat breaks out he jumps in until he takes damage of any kind and then he runs away, possibly yelling for a cleric. I've seen it in D&D, Shadowrun (think that was vampires too, and he was a cybered-out Elf), Traveller (don't want to scratch the battle dress - I think we teased him about it being more of a battle-skirt given his attitude) Gamma World, Twilight, etc. Pretty much any game we played in the 80's and 90's this player had the same character. He did play a necromancer once in 2nd edition and that partially solved the problem - he had minions he could send in to fight and some kind of teleport thing to get him out of danger if his robe got dirty in some way.
Anyway I might call this the "Power Coward" if I was pressed for a name. He's a lot like a Power Gamer but he's not interested in testing it out - he already know his creation is the baddest and he doesn't want you to scratch it or get it dirty.