How does the trademark system work?

It depends on how unusual the real name is. For example, the web site Hotjobs.com tried to trademark its name, but it was determined that "hot jobs" was "too generic" to be trademarked. No harm in trying, though!

You're a man who repairs computers; thus "The Computer Repairman" describes your service and not your identity. You can't trademark it.

Whether or not you could otherwise trademark it, you certainly can't when someone else is already using it for a similar business in the same area (which area is effectively the entire world, since you've chosen the .com domain.) Unless maybe if you get a big team of very highly-paid lawyers on your side, and the other guy doesn't.

There would be very little difference between "COMPUTERREPAIRMAN" and "THECOMPUTERREPAIRMAN" in terms of getting a trademark. A trademark on either one (if you could get one, which is unlikely) would cover both.

Are you sure the people with "the" at the start aren't just trying to sell you the domain? There are plenty of people who do that. Check out COMPUTERREPAIRMAN.net, COMPUTERREPAIRMAN.org, COMPUTERREPAIRMAN.biz and so on. I bet they're all registered to some domain-squatting outfit in Canada who will sell you the domain at an enormous markup.

Is "thehitechhandyman.com" linked in your profile the site in question? Kudos on not self-linking and all, but I think people will be better able to answer if they know the specific name.

"The Hi Tech Handy Man" is slightly more likely to be trademarkable than "The Computer Repair Man", but you may run into issues if the person without the "The" starting using the name before you did. Consult a lawyer if you a serious about federally registering your mark.

I'd say your best bet to protect your company's identity would be to buy the domain from the current owner. Say you are talking about hitechhandyman.com. It's basically a barren text page advertising generic computer services that can't be doing anyone a lot of good. http://web.archive.org/web/*/http://www.hitechhandyman.com/ shows that the site was even more boring in the past. WHOIS tells us it is owned by TheCapitol.Net in Virginia. That website appears to be for a political education firm of some kind, so I doubt the computer service advertised at hitechhandyman.com is their core focus. By all this I mean to say that you could probably make them an offer and have a fair shot at it. Then you've got all the domains under your control and the good people of Michigan will be spared any undue confusion.

The computer repair man is an example. He doesn't reveal the real name. I'd assume its more unique. First off, many business can have the same name and similiar URLs. Your example sounds bad for you as they are the pre-existing company. None of this should really matter. This is a non-problem and assuming your businesses identity is at risk seems to be going a bit too far. If you truly feel that this other group is being mistaken for your company then you are free to change your company's name. I don't think getting a trademark will make any difference. If they have a similiar trademark and you want to contest it, the http://www.uspto.gov/web/offices/tac/tmfaq.htm#Other002. As far as demanding their URL, well, you're at the whim of ICANN for this. You can read their rulings http://www.icann.org/udrp/Detail167.htm.