I think the new format for rare and epic items having unique names like “Havoc†instead of the mouthful of something like “Destructive Axe of Life†is a great change. So here's a bunch of suggestions for more such names. I hope there's dozens of names for each item type in the final game to minimize seeing the same name very often.
It would also open a lot more freedom to make certain modifiers (particularly legendary ones) have a chance to give items a specific names. Say, a legendary +Fire modifier on an axe would give it a chance to be named “Lava Chop†or something.
Anyway, here are my more generic suggestions. Some are a little silly, but hopefully not too much.
Wands
The End of the Rainbow
Kaleidoscope
Prismatic Fury
Deluge
Leprechaun's Revenge
Astarte's Breath
Geyser
Torrent
Void Ripper
Staff
Conduit
Storyteller
Prometheus
Unassuming Smackdown
Shine and Shadow
Third Leg
Buddy
Magic Slap
The Poetry of Death
The Balancer
Fissure
The Churn
The Sting
The Bird & The Bee
Axes
Tumult
Amputator
Cacophony
Limbsnatcher
Battle Laugh
Crazy Eyes
Damaged Goods
Gristle
The Feast
The Hunger
Fleshmunch
Death's Employee of the Month
Hope Ender
Tearjerker
The Comedy of Terror
The Beckoning
The Drudge
Swords
Quillspill
Prayer
Riposterizer
A Thousand Cuts
Giantfell
Death's Thrust
Dancing Death
Stalagmite
Problem Solver
Diplomacy
Paladin's Pal
Hordeslayer
The Blood of Hope
Blessed Agony
Hollower
Artist of Pain
Maces
Pestle
Pastemaker
The Inquisitor
The Bonk
The Beat
Squishy
Breathstealer
Bonesnap
Anaconda
Gravity
Sandman
The Great Sleep
Dazey
The Wham
The Mountain
Avalanche
Rockslide
Starmaker
Ouch Master
Lights Out
Blackout
Homogenizer
Clonker
Lung Squeeze
Echo Maker
Daggers
Backscratch
Spinetickler
Hair Raiser
Kidney Magnet
Etch
Twirl
Ritualizer
The Last Laugh
Deathpoke
Shadowbite
Stabbey
Cruel Caress
The Mistress
Gleam
The Chef's Mess
Toothpick
The Surprise
The Bad Gift
The Secret
The Giggler
Zig Zag
Zester
Scar
Sufferstop
Smile Ender
Witch's Grin
Spears
Vaulter
Long Poke
The Distance
The Coffin Nail
The Thrust
Baykeeper
Deep Death
Shieldsplitter
The Heave
The Hearse
Beginning Ender
Blight
Shields
Best Friend
Flagbearer
Burden Bearer
Herald
Deflector
The Rejection
Denial
Eternity
Generous Menace
The Gift that Keeps on Giving
Emancipation
Black Mirror
The Emasculator
Indifference
Blade Cushion
Pincushion
Exhauster
The Jammer
Something in the Way
Loyalty
Rings
Heritage
Storyloop
Hategem
Divorce Ring
Gangrene
Brass Knuckle
Truthspool
The Bling
Jealousy
Index Codex
Finger Portal
Mobeus
Band of Music
Demon Circle
Ritual Ring
Halo
Shackle
Quest Tug
Amulets
Neckmunch
Vanity
Shard
The Masseuse
Drowner
Breath Thief
The Worm
Labyrinth
Sharksmile
Fractal
The One's Friend
Soul Mirror
Companion of Hearts
Idol of a Dead God
Cruel Prayer
Heart Tickle
Fate's Haven
Helm
Scalp Dancer
True Sight
Incubator
Dream Thief
Mind Cage
Thought Box
The Calm
The Sixth Sense
Sniper's Eye
Curiosity
The Crying Smile
The Quip
The Gaze
Droolcatcher
Peek Peak
Headhugger
Smellkeep
Head Case
The Echo
Gloves
The Snap
The Clap
The Slap
Second Callous
Instrumentium
Bloodbrushers
Sweeps
Crushers
Slicers
Dicers
Grippers
Snippers
Pilchers
Snatchers
The White Knuckles
The Flick and Tickle
The One-Two Punch
The Last Smack
Knockout
Lifters
Belts
Soul Core
Bladebelt
Toolspool
Chastity
Pants Dancer
The Professional
The Long Haul
Boots
Roundhousers
Coalwalkers
Imp Kicks
Wiz Kicks
Stompy
The Squish
Whisperstep
Cloudstep
Dancers
Prancers
The Jaunt
Questers
Quicksand
The Steep Leap
Cliffstickers