I think you want to know whether you can force the owner of company.com to transfer that domain name registration to you or, if not, whether someone else can lawfully purchase and use it for his own website.
Because the owner of company.com registered that domain name before you created trademark rights in "Company," you may not use the UDRP arbitration process to challenge its ownership of that domain. You may, however, use the federal anticyberquatting statute if your own trademark attorney believes the facts justify the claim.
Until a court concludes that the owner of company.com is not its rightful owner, yes, the owner can lawfully sell that domain name registration. To anyone. Can that person lawfully publish a website at that domain? Likely not so long as you, in fact, can demonstrate that you have created trademark rights in "Company." Your failure to register "Company" with the federal trademark office makes this harder than it would be had you registered. But the registration is not required.
You need to have a California-licensed trademark attorney review all the facts, and your business, to provide you with general branding advice and specific advice about this domain name matter. That attorney can also help you clear the rights to your company logo and, if cleared, propertly protect it. Good luck.
The above response is general information ONLY and is not legal advice, does not form an attorney-client relationship, and should NOT be relied upon to take or refrain from taking any action. I am not your attorney. You should seek the advice of competent counsel before taking any action related to your inquiry.
I am glad that you are seeking competent legal help with this issue. The bad news, however, is that you will not find the answers you are looking for here because yours is a very fact intensive scenario. Any of us will have more questions than answers at this point and while I am tempted to offer a run through some of the considerations, I think this may cause some confusion. The bottom line, however, is that whoever was using the mark first in your market area will likely prevail, but the analysis of goods and services needs to be conducted along with the "in use" analysis and this is not something you can figure out on your own.
I suggest that you consult with a lawyer in private and discuss your objectives in more detail. You can start by calling around to several for a free phone consultation, get some insights then pick the best fit to work with.
DISCLAIMER: this is not intended to be specific legal advice and should not be relied upon as such. No attorney-client relationship is formed with the law firm of Natoli-Lapin, LLC on the basis of this posting.
There are several different strategies you could pursue, from hardball to softball.
You might try registering your service mark, and based on earlier use in commerce, send a cease and desist letter to the other firm to protect your mark.
You could work out a co-existence agreement with the other company.
There are other options, but you will be able to discuss them and strategize with your future attorney.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
Your legal right you need to exercise is the right to hire an IP attorney to protect your other legal rights, and that is how you best protect your logo. This is your company name, the crown jewel of your company assets (think of what is the most important asset of Coca-Cola, Apple, SONY, Ford, Toyota, Chevy, Maytag -their company names). Don't go cheap. Get off this free advice site and get into an IP lawyer's office so this is done right. For San Mateo, I would recommend Glenn VonTersch http://www.avvo.com/attorneys/94002-ca-glenn-vontersch-147315.html
Frankly, I doubt you are going to get this other business to stop using the name or to change domain names. I think that to have any chance you will need to jump on them hard and quick, very aggressively to make them think you are going to spend whatever it takes to stop them. That may cause them to reconsider the economics of the matter. Of course, if they hang tough you could spend a fortune in legal fees on this and perhaps lose in the end. It is a call for you and you lawyer to make after a thorough investigation of this other company and their finances. Hopefully they are operating on a shoestring budget and cannot afford to fight you. Unfortunately, since you are here asking for free legal advice, I suspect it may be just the other way around and may be YOU operating on the shoestring budget unable to afford the fight.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.