This was, by far, the most hilarious batch of suggestions I've collected on Cockeyed.com. Here are my picks for the winners. The first five are superb!

Unitard Edge
Platinum Rush
Power Point
Republicans
Team Ramrod
Profit Lava
Omni-Steal
Businesense
Shoulderpad
Urinary Tract Infection
Qliche'
Shark Jumpers
Ulcercorp
Vas Deferens and Associates
Karma
Coinstar
Two Pay
versacorpse
Billionhair
Mariachi Dentistry
team fresh
Mangina
Whorex
Omnivore
Biznatch
The Smartinators
Voltron
Desecrate
mBezel
Mxyzptlk
AGreed
Vandelay Industries

I'd also like to salute the following superb batch, which will, no doubt, pop up as actual company names, MLM schemes or Apprentice Team names:

Adept
Alpha Squad
Aura
Bonaparte
Bottom Line
Brilliantech
Bull Market
Centurion
Compliment
Compound Interest
Conexicorp
Crescent
Domina
Dynacorp
Edgenet
Effica
Engenda
Envizion
Exelcorp
Expertise
Firmuscorp
Ideation
Intelgia
International Trust
Interslice
Laser
Lexicon
Lucre
Lux Enterprise
Macrosoft
Maxcess
Megavest
Montego
Net Gain
Omnara
Paradigm
Pinnacle
Primeoptima
Proactive
Prospero
ROI
Silversmith
Skyward
Stratecore
Stratosphere
Summit
Supacorp
Superium
Synthelion
Toolbox
Top Shelf
Torque
Trident
Tripex
Trumpet
Utilicorp
venti
Veritas
Versaquest
Versimilitude
Verti-go 
Xenith
Zephyr

Thank you for all the fine suggestions! These were hilarious!

You can also check the complete list of Apprentice Team name suggestions.