I have a spear mod which gives me a daedric spear. Its got the Chaos enchant and fiery soultrap. I call it Soulstorm. My Dragonbone one handed axe is called spirit. (Same enchants).
Going on a slight tangent, my Familiar's referred to as 'Boy' while My flaming Familiar is 'Girl'. I don't use the others.
Repentance: Silver Sword enchanted with Banish and Turn Undead. I mainly use this Enchantment for Healers/Mages.
Dagon's Wrath: Daedric Sword enchanted with Fire damage and Fiery Soul Trap. I mainly use this for more evil characters.
Sheogorath's Fury: Ebony Dagger enchanted with Chaos damage and Fear. Used mostly for Illutionist or Mage characters.
I start out with appropriate names, like Van Helsing's / Buffy's / Robin Hood's whatever. When I run out if them I'll use characters form whatever TV I'm watching. There as lot of rings around here with names like Jon Snow, Ygritte, Little Sam, for instance. Then it's whatever artist is on shuffle play on my 'phone
I once had fun trying to find famous fish to name rings of underwater breathing
The gear I always make names depending on what I'm playing as like Volkihar Gauntlets, Legate Armor etc.
But the weapons I have a strict only black soul gems policy so I have to insert the name of whatever persons soul is inside the gem to the weapon name. Example:
Step 1: Murder Ulthgerd the Unbroken
Step 2: Capture her soul in a Black Soul gem
Step 3: Use her soul to enchant a Steel Sword and call it Unbroken Steel Sword or simply Ulthgerd and place it in a rack so you remember you killed her to enchant a weapon you never even use.
I like to draw on the languages from the works of J.R.R Tolkien for my weapon names. For example, "Charcauth". It's Sindarin Elvish for "War fang". With armor I usually go with something that belies its' use, or give it a name that implies that it's no ordinary armor. Like for the Dawnguard light armor, I named it "Rohhirim [armor piece]". Hmmm... maybe I should work on some LOTR based builds...