Can you get the rights to a registered domain if you own the tradename?
Tradenames are not in the same legal class as Trademarks or
Copyrights, and as such do not hold the same legal weight. For
example, you can have companies with the same tradename in
different states, each having their own legal protections.
Trademarks afford more stringent legal protection, and as such if you own a trademark and the domain registrant is using the name you may have legal recourse. However, for all but major brands/trademarks, such legal recourse is expensive and not always successful. If the domain registrant can show that they have a legal reason for using the domain name (they own a tradename in their state, or they own an incorporated business with a similar name, etc.) then trademark protection involving a domain name may not apply. Also, tradenames and trademarks only afford legal protections in the country of origin or in those countries where it's registered. If the domain holder's site is based in another country, you have no recourse.
Trademark protection for domains are generally only successfully challenged by corporations or people who have international trademark and copyright protections. Examples are actors (whose names and images are copyrighted) and major international corporations like Sony, Coca-Cola, etc., who have established their trademarks in most countries on the planet.
You can always make a bid for any particular domain on the Registrar's site where the domain is being maintained. For cyber-squatters (less common today than they were 10 years ago since laws have changed) it's easier to come up with a minor variation on the name rather than go through the legal hassle and expense of giving them what they want. Many major corporations with major trademarks do this on a regular basis.
Also, you can add your name to a domain watch list on most Registrar sites, which will notify you when a domain becomes available or is placed for sale.
Having been in the web hosting and design business for 13 years now, I can tell you though that domain names aren't necessarily your biggest asset. While your tradename/trademark is a big asset, site traffic is largely driven by traditional advertising or paid Search Engine ads. "Register it and they will come" is a fantasy - follow that and you'll join the many thousands of hopefuls who failed to realize that like any business, a website requires that people know about it, and to know you need to tell them - business cards, brochures, flyers, etc. No modern business with a web presence today distributes any company material that doesn't have their web address on it. Even in TV and print ads, domains are always displayed.
The "Trademark Cyberpiracy Prevention Act" deals with domains and registered tradenames/trademarks. The law basically makes it harder for someone or some group to perform what is known as "cyber squatting." Basically it gives companies and individuals an ability to fight a "cyber squatter" in court. The unfortunate fact is that to defend this case, you most likely will have to hire an attorney to represent you in the court that has jurisdiction over the case matter.
Another problem that often arises is that ownership of tradenames is different from trademarks, and both of these may be of only local or federal significance. The Internet is global, and it would be difficult to enforce a local tradename in a remote region where the company does not do any business. In other words, just because you own a trademark or tradename in the U.S.A. does not give you any particular right to stop others from using the identical mark or name elsewhere, or from registering it as a bona fide domain name on the internet.