Personal Mook

Candace: You'll be my henchman!

Stacy: What's that?

Candace: It's like the bridesmaid of crime.

— Phineas and Ferb, "The Beak"

Sometimes, villains have henchpeople dedicated to particular tasks.

Such as:

They will have more personality than your conventional mook and may even be The Dragon.

Examples:

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Comic Books

Sin City has Manute who started out as Ava Lord's bodyguard, driver, and The Dragon.
- Also, even though Blue Eyes is a mook assassin herself, she often uses a lumbering mook named Gordo to do a lot of heavy lifting.

Film

James Bond
- Big Bad Goldfinger had Pussy Galore for his personal Pilot and also as the instructor for his own personal airforce.
  - Oddjob is his Battle Butler and chaffeur.
- Scaramanga's assistant Nick Nack is his personal chef and waiter. His job is also keep him on the edge by hiring killers after him.
- Stromberg from The Spy Who Loved Me had his personal helicopter pilot Naomi.

Literature

World Without End's prospective antagonists have their own, Godwyn has a lick spittle, Philemon, who has no real uses other than another person to make hear Godwyn talk. Ralph has the more useful Alan Fernhill. Ralph seems to be the older version of Alan.

Live-Action TV

Both villains who served as The Dragon in Kagaku Sentai Dynaman had their own Mauve Shirt who acted as their personal assistant. Megiddo had Gira and Geel, who aided him in most of his schemes, and Zenobia had Bilgis, whose job was mainly to carry Zenobia's staff for her.

Professional Wrestling

Dalton Castle has two Vegas style twin show boys in peacock masks to attend hand and foot to his every need. Well, he has several of them in Ring of Honor, but usually only relies on two, who helped him win the World Six Man Tag Team Championship belts. The rest are just red shirts called for when more bodies are needed for menial tasks.

Video Games

Scarface: The World Is Yours has lackeys that range from highly intelligent NPCs to ones the player can control. Calling for a boat or a car will gain a driver that will follow and kill for you. There are also the Assassin, Driver (note the capital) and Enforcer. All have differing tasks...if you choose. All can assist Tony (the player) in multiple ways, such as slaughtering bothersome gangs or making cash. Oddly, the last three can kill regular citizens, unlike Tony. Many of the NPC mooks, like most citizens of Miami, have unique dialogue with Tony, this giving character development.
Evil Genius gave the player character a colorful personal bodyguard once they reached certain levels of Notoriety.
World of Warcraft Cataclysm gives us the Lumbering Oaf, which serves Helix Gearbreaker, acting as a guardian and mount for the evil little goblin. The Oaf must be defeated as phase one of the Gearbreaker boss fight, and even has his own special move where he throws a fully voice-acted tantrum (which is odd for unnamed enemies) and slams a player into the wall.
The Godfather 2 allows you to recruit these for your own Badass Crew. They have special skills that will come in handy above and beyond their superior stats to the standard Corleone mook/redshirt.
Adrian Ripburger in Full Throttle has two henchmen, Bolus and Nestor, who act as his bodyguard and his driver, respectively.

Web Original

In Sunset Paradise, the Goonies are Sir Benedict Cumbersnatch's principal enforcers: because he's been reduced to a living egg, he needs them to do the dirty work and even to transport him. The personal one is a blue Goonie who carries a monitor and corrects the Spud Buds for Benedict in the pilot, then transports him since the episode 6.

Western Animation

We have Hammerhead's unnamed Chaffeur(ess?) in The Spectacular Spider-Man. Hammerhead himself starts out as a Dragon-flavor of this to Tombstone, seeming to exist solely to relay the boss's orders to the mob so he could maintain his front as a Villain with Good Publicity. After Tombstone starts questioning his competence, however, Hammerhead becomes The Starscream and, ultimately, the Green Goblin's Unwitting Pawn.
Lex Luthor of Superman: The Animated Series had his valet Mercy.
Owen Burnett is David Xanatos's general assistant on Gargoyles. This is because Owen is actually the fairy Puck, who first approached Xanatos in this guise and offered him a wish. Xanatos, recognizing the competence and usefulness of the Owen persona, wished for a lifetime of faithful service from him.
- He was impressed enough that he never tried to pull any of his usual tricks on Xanatos.