This may seem like a silly suggestion to some, but
doodle!
Here at work, when my eyes get sore from trawling the DS Forums, I pull out a little pad and a pen, and I doodle. What do I doodle? Shadowrun Megacorporate Logos.
Now, I don't nescesarily know what I'm gonna do before I start, so sometimes I start with an artistic theme, sometimes with a letter.
Once you have something that looks like it would go nicely on a letterhead, make a name to match it.
Obviously I can't reproduce the logos on here, but on the last two pages of my little pad are: Tower Industrial Electronics (based out of the Tower of London, no less...

), Northstar Cybersystems Inc., Crisis Medi-Corp (Brit version of Docwagon), Optek Surveillance Technologies (small corp, but very high tech) and Sigma Information Technologies.
The first and last are "regulars" of mine - representing, respectively, a Bad and a Good corp. Well, as good as any corp can be.
I am particularly proud of my first ever S.I.T logo - a cartoon puppy with a datajack and a cyberdeck.
"Sit, Fido!"