I'm looking for a new "B" name to replace Banshee Company. What do you think would be a good name for this company?

My suggestion is to poll the troops in your new Company. I'm sure they all have ideas of what they'd like to have as their designator. After all, it's THEIR Company as much as it is yours. Ultimately, it's your call (assuming Higher agrees). You could even use it as an opportunity to get to know the troops and get a feel of how things are going overall in the unit.

You could go off script. When I was in Charlie 2-64 Armor, we were changed from Cobra to The House of Pain. Callsigns were Painful 6, 7, etc.

grizzly bears because of their devastating power

Battle Masters of the Universe, Barbarians, Beasts, Berserkers, think about what you'd like you'd like your call sign to be , battle cats probably not a good choice. That being said, poll the company and you the 1SG, PLs, PSGs can pick it. I let my platoon decide on our logo and name during my last Iraq tour, we ended up as zombies which is more a state of being than a title. It raised moral, built a team and we had awesome t-shirts and coins made.

Since 1-37 used to be stationed in Friedberg, I would suggest Blitzkrieg or Blitz. Bandits is the BN call sign, or at least it used to be, so don't think that would work.

MAJ (Join to see)
Considering that in Celtic mythology Banshees were women, I can understand why some might not like the nickname?
First, we are still the Army so, not important what they like but that is a different discussion.
Berserkers and Bloody Bastards have a nice a ring to them?
Since you are talking armor...Black Horse, Steel Boars or Iron Bears as composite ceramics just does not have the right ring to it?
Jordan's Berserkers?
At least there is some food for thought?

tongue in cheek:
Bozo
Bubah
Bruins
Ballsy
Blushing
Bovine
Barbiturate
Bone
Byrd or Bird
Bigly
Bonehead
Buffalo
Bored

MAJ (Join to see) I am very surprised you are being giving the option to change the unit name... There are second and third order effects of changing a units name that are a pain to deal with as well as real $$$$ costs to a name change. Ive never heard of a company commander having this authority.. Ive had Bde CDRs come into a unit and direct "Apache" company in 2nd BN get a new name. Ive seen Div G3s recognize that he had three "Bulldog" named companies in the unit command they manage and direct 2 of them change before deployment...
But never a company commander walk in after being giving a command assignment and just deciding to change the company name.

All that to say, you should feel lucky Sir, its a rare opportunity. So don't screw it up and name them Bambi or Bumblebees or the like. ....lol

If it's available, Bandit for this....
"On 12 July 1944, the Battalion landed at Normandy and began combat operations in the European Theater of War. There it fought with great distinction in the Normandy, Northern France, Rhineland, Ardennes-Alsace, and Central European campaigns. For its actions, the Bandit Battalion earned three French Croix De Guerres and a Presidential Unit Citation"

Or How about Bastogne or go against the grain with Thunderbolt for these reasons..
"Among the 37th Tank Battalion’s most notable actions were seizing crossings on the Marne, Meuse, and Moselle Rivers during the Third Army’s historic drive across France, and the relief of the 101st Airborne Division encircled at Bastogne. The most notable commander of the 37th Tank Battalion was General Creighton Abrams (commander of military operations in Vietnam and later Army Chief of Staff) who command the 37th from Normandy to the end of the war on his tank “Thunderbolt.” "

Or you could go with something Elvis related...
"Task Force Bandits drove Al Qaeda in Iraq from their sanctuary and inflicted grievous losses on the enemy. For these actions, the Battalion has again been nominated for a unit decoration. After a 45 day extension, the Battalion returned to Friedberg in February 2007 to begin its final mission: inactivation. For more than sixty years, there have been American tank Soldiers in Friedberg who called themselves the Bandits. This tradition began with the 1st Battalion 32nd Armor, with whom Elvis Presley served in the 1950’s."

http://www.bliss.army.mil/2hbct1ar/1-37ar.html

Bandits