Sigma item name suggestions:

[GregMXL]

Self explanatory. Stick with Diablo lore. Anything idiotic will be deleted. List names and a short description afterwards. No item stats, just names for now and you can list for what specific item name it should replace if you want.

[Kaljurei]

Pasting my runeword suggestions for Weapons here.

Ok here's my list of suggestions.

Weapon Runewords -

Dawn - This is fine. It's a good starting runeword and gives Light Radius so synergizes well.
Shark - Don't see how Sharks get bloodlust on killing someone. Maybe if you changed the proc to Bloodlust on attack/striking it would make sense.
Enyo - As a consort to Ares, this is not a bad name for any weapon.
Azrael - This is the name for the Christian Angel of Death and in DC Comics, he's like Ironman really. Maybe change the proc to something else, which does physical damage and you have a name with good synergy. Don't see why this weapon has FCR and Fire Resist though.
Void - Boring name but I don't know what else you could put here.
Oblivion - The only reason this name would ever fit this weapon is because you have Abyss o-skill charges on it. Instead of Venomous Spirit you could rather have Singularity proc, as you know a Black Hole basically sucks everything in and there's no escape from it. Remove the poison damage as well, and make it Phy/Mag damage increase.
Berith - Ok I searched the web a bit and all I could find was that Baal was also called Baal-Berith. In that sense the gold find number is appropriate, but not sure about the rest. Don't get me wrong, it's a nice item, but maybe you could have some of Baal's skills as an O-skill or an on attack proc, like Mirror Image(Use D2V's Decoy) or reanimate as the monsters he summons.
Gehenna - Apparently another word for Hell or Purgatory. Not sure why you would have a Cold spell proc considering Hell is supposed to be HOT. Maybe change the proc to Apocalypse, give Fire Spell damage. Leave the poison as it is I'd guess. You could just change the name also I guess and perhaps replace it with some kind of a sea creature that lives in the depths and has a poison attack.
Triune - Very apt name considering the stats and values. But just, considering that it refers to the Holy Trinity, you could add maybe a reanimate chance of 1% for 3 mobs that resemble the Holy Trinity. Holy Spirit could be Gloam, no clue what you'd put for God and Jesus.
Adramelech - Apparently a sun god(demon) who people sacrificed their children to using fire, and looks like a goat with peacock feathers. Everything seems to fit the name although I'd wonder why would anyone want to make this item, it's not great.
Archangel - Ok a weapon named like this has a lot of potential. Don't remember/know how a Moon Knight looks like(Oblivion Knight with a spell orb in right hand?). It has good damage, extra damage to demons(Should also be Undead). I'd replace the reanimate with a good chance to reanimate Ni'Va, so that you're shielded occasionally in Sacred Armor(or whatever it casts when it dies), very nice for a Summoner build, a bit OP maybe. Um, could probably add an O-skill that causes you to glow and does constant damage in AOE(not sure which element, possibly fire, you know..Seraphims, like Sanctuary Aura), maybe even sprout angelic wings Twisted Evil
Dumpweed - Ok I guess you were just rushed here to make the name lol. Item seems really bland and boring but great mods, so I'd say rework the item completely and give it an appropriate name.

I'll come up with more suggestions later. Sorry if I came off as changing the item to fit the name rather than vice versa, it's hard to do that unless you have an idea of what you want the item to be and then name it.

Also, in the book Demonsbane, Siggard(the protagonist) finds a sword named Guthbreoht. Properties of the weapon - The sword sang to Siggard each time he needed to do battle, and gave him strength. He could also speak in an unknown tongue using battle cries to rouse armies and slay demons. The song became stronger with each demon killed. He could sense invisible demons when wielding the blade. The sword was really strong, as he could kill demons with one stroke. The song also changed tune and effect depending on the situation for ex. in a battle it could make Siggard stronger and faster, in a peaceful situation it was soothing and gentle. It also was the only weapon that could destroy some of the invisible demons who were immune to all elemental magic. Siggard also used it to kill Assur, but that was more due to the fact that Siggard was the only one who could break the Seal of Invulnerability that was cast on Assur by Diablo.

There's also Siggard the character himself, so an item named say "Siggard's Undying Vengeance" or "Siggard's Undying Defiance" could be an appropriate name for a set item. There's also Sarnakyle in the same story who was eventually called the Red Wizard, who taught the Mage Clans various secrets of Elemental Magic after they discovered that they could no longer summon demons or control them and almost lost the war against Bartuc as a result, so some item named on him could also be used as a Set item. Maybe a few new sets?

[Aspirine101]

Brainstorming...

names:

[Soponator]

Hadriel's Protector - pally weap
Natalias secret - sin claw
Akara's eminence - helm or sorc body armor
Blood Raven's judgement - Zon Bow/helmet.
will add more when i have more time. will come with more neutral stuff for RWs

[axios]

Gift of the Goddess-staff
Demonic Weakness-2h wpn   
Retribution-gloves
Mark of the High Heavens-amulet
Abomination-pally 2h
Wind Runner-boots
Titanic Struggle-shield
Darkness within-armor
sacrilege-armor

[Wotan]

Current Wotansvolk name could be used on a spear/polearm.
Bul'Kathos's Will replaces Wotansvolk as SSU Labrys with slight stats changes, but thats a discussion for another time.

[Str0b3l]

Boot of Hermes --> explains itself
Daedric Crescent --> Morrowind GG
The Butcher's Cleaver --> WOAH FRESH MEAT
judas betrayal --> HueHueHue
Bear Grylls Survival Blade --> Bear Grylls no words
Lightsaber --> BZ BZ BZ
Jigsaw's Trap --> SAW
Freddy (Krueger)/Wolverine Claws
Jason's Machete
Mjölnir - Thros Hammer
Helm/Armor of the nemean Lion --> Hercules

[Aspirine101]

^ I support Mjolnir
also Gungnir

[Wotan]

^ I support Mjolnir
also Gungnir

Self explanatory. Stick with Diablo lore. Anything idiotic will be deleted. List names and a short description afterwards. No item stats, just names for now and you can list for what specific item name it should replace if you want.

Diablo's lore is rich enough to rip-off names of Norse religion.   

[Aspirine101]

Well, considering laz also made a lot of non-diablo lore related names, I guess they're ok.
@ripping names from norse religion, there is a bow (made by laz) which is called Gjallarhorn.

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