Let's see, taking a few of them and putting my tongue in cheek... :P
Caveman Company. Not the most sophisticated of the mercenary commands in the Inner Spere, you can rely on them to take down the mammoths of the age: they specialize in assault mech hunting through ruses, traps and ambushes, where their smaller mech use coordinated attacks tpo down them. The Cavemen have been the bane of more than one company that though itself safe under all those tons of armor. Their use of firestarters to shut down assault mechs is legendary.
Cogburns roosters. A mercenary command that has taken to the clan approach of Batchall and use it as frequently as they can. They are also one of the biggest tall story tellers you will find in the IS, with Valkyrie pilots explaining how they take on Stalkers on a weekly basis.
Legio Testudo. A company of Lyran descent, the legio testudo is famous for turtle-ing it out. They are great at securing a location, but tend to be poor raiders or reserve units, taking a looooong time to assess the threat and intervene. Few people can sack them from a defensive position, though.
Old Soldiers. A small command formed by veteran mechwarriors. The unit recreuits from mechwarriors that are deemed too old to serve in more active units. While there are 2 heavy lances in the company, they are generally hired as advisors, where their experience in warfare is paramount to the HQ more than as combat troops.
Hell’s heartbreakers. A unit of young dashing mechwarriors. Boast a lot, drink more, have to run from more planet when the daughter or son of the ruling family elopes. Their combat record do not support most of their boasts, but they are cheap and easy to convince to come as long as you write “girls” and “booze” in the contract.
Gandalf’s Merlins. A periphery merc unit boasting a lot of the aforementioned mechs. They say they can play magic with them. They are rather new to the inner sphere, so that claim is still unsustained.
The Zombie Army. A force of assault mechs and hunchbacks. When they are committed to battle they are not the fast units, but a good front line regiment. They go in regardless of casualties. They kill stuff. They go out. All of it like they do not care. Reliable if simple in their tactical approach.
Myrmidons. A reliable unit. Like their namesakes, they use a lot of heavy mechs, specially Zeus, Cyclops and Ares battlemechs. Their unit commander rides in Achilles, a Zeus mech that has never been downed; even if he is a great mechwarrior, he is somewhat overconfident, leading from the front at all times.
Devil’s Doughboys. A unit renowned for their great appetite and even greater power abuse when it comes to the local population. Still, they are what you need when there is a pirate raid. Their blue mechs and “Law and Order” policy does not tolerate breakings in their contract or the interests of their employer. LCivilian populations might not agree 100%, but so is life.
Drop bears. A unit of drop infantry and VTOLS specializing in high risk nocturnal drops in or near key enemy locations.
Feral Ferrets. A unit renowned for their primal and savage defence tactics, not giving quarter nor expecting it when they are assigned a location to defend.
Stalkers. A recon unit. Use a lot of long range communications equipment. Being of capellan origin, they are one of the few mercenary users of the Swift Wind car. Their attack taxctics tend to deal with attacking clearly inferior targets with overwhelming force, usually with rapid insertion. Have a no survivors policy.
Men With No Name. A company coming for Eastwood, a penal planet. How they cgot their mechs is quite unclear, but none of the pilots has ever told their name to anyone. Might be their fellonious past or a policy. The leader is known by his nechwarrior name: Blondie. Surprisingly for a hard hitting unit like his, Blondie pilots a Clint.