How many of you actually rename your equipment/weapons?

I do.

Do you name them after your characters or do you have specific names?

If it's same sets of armor that I'm making for my character and a follower I'll usu put their names in them. If it's a set of like Tavern Clothes or Noble Clothes that have Fortify [magic_school] on I usu name them after the school. The normal Noble Clothes that my Assassin Chick wears when she's in towns or around 'people' are called Pirate Princess Robes, Pirate Princess Shoes, and Pirate Princess Circlet.

I always name my equipment and weapons. One of my favorite things to do. I just enchanted a Daedric dagger with Soul Trap and named it Dagger of the Damned.

Sometimes I title my armor with my character's name like Xerxes' Armor or Riddike's Helm. I usually give my weapons a particular name that sounds cool.

What a cool idea!

Yeah, That's about what I do. Sometimes all go look up old medieval words, Gothic words, Etc

I name some of my weapons after my real life friends. I name clothes after the jobs i do, i have a full set of foftify smithing clothes, alchemy etc! The main reason i stick just a little enchantment on something is so i get to name it.

I do but recently I'm more into the generic names except for a few things like my firey soul trap enchanted Dragonbone Sword (A Pyromancer's Dragonbone Sword)

I do when I enchant weapons or armor. Nothing to fancy though.

For example Leather Armor would be renamed Leather Armor of Health if I added a health enchant. Its easier for me to find stuff that way when storing.

I put Soul Trap on one of the Shivs I brought out of Cidhna Mine and called it Soulstix. The Daedric Dagger that I carry (only equip it when I need to fill soul gems) I renamed Daedric Dagger of Soulace.

Before I stopped enchanting weapons (didn't need to because I get plenty of damage from my improved weapons) I put Absorb Health and Fire on it and I called it Daedric Sword of Flaming Health and on the other I put Absorb Stamina and Shock and called it Daedric Sword of Shocking Stamina.

Thanks. I do what I can.

A few examples:
Gloves of Heavy Smithing
Gloves of Heavy Alchemy
Circlet of Underwater Alchemy

I'm sure y'all can guess the enchants.

Edited for accuracy.