There is not enough factual material to begin to analyze, especially since you are intentionally shielding facts. It seems to me you actually prefer to do your own lawyering, so I am not going to recommend you hire counsel, even just to get advice.
Licensed in Maryland with offices in Maryland and Oregon. Information here is general, does not create a lawyer-client relationship, and is not a substitute for consulting with an experienced attorney on the specifics of your situation.
They may not "personally" serve you (the company). The plaintiff can still serve you "by publication" and you will have virtually no chance to have personal knowledge of the service. They will obtain a default judgment against you, wait six months until the default cannot be set aside and then execute against whatever assets the company may own.
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.
If they are persistent, they will recognize the mistake and sue the right company, even if it requires an investigator's assistance and a new suit. Companies are registered with the state and list an agent for service. They will serve your company and likely you (by publication if needed), and then they can collect on your company, perhaps putting into bankruptcy if they persist. Will they - dunno. Better get an attorney if your companies have any assets.
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.
Short answer... if they don't serve your company, there is nothing that they can do in court. However, as others have noted, they might serve by publication. Good luck!
I am an Attorney-at-Law, licensed to practice law only in the state of California. Unless we have both signed a formal retainer agreement, you are not my client, and my discussion of issues does not constitute legal advice. Opinions expressed herein are those of the author, and do not necessarily represent the opinions of those who hold other opinions.
If your company is not named and your company has not been served, then you are not a party to the lawsuit. Presumably, at some point, the other company will be served and will respond, by way of demurrer or motion to dismiss (you didn't indicate whether this was federal or state court and where the action was filed) stating that they are not the correct defendant. At that point, the plaintiff will either amend or refile correctly identifying your company and WILL you get served. In the interim, you should check the court's docket and see what has been filed. If, at some point, you see that your company has been named AND there is a proof of service, then you had better respond or you will be defaulted.