united-states
Now, Alice only knows Bob's name. This is insufficient to take legal
action.
If you have his name, you can make him a defendant in a lawsuit. This and what Alice knows is sufficient to bring a breach of contract action by filing a complaint in court. Filing the lawsuit preserves any applicable statute of limitations, even though it may take some additional time (subject to its own deadlines) to actually deliver the legal papers to Bob so that the lawsuit can go forward. The act of delivering the necessary legal papers to Bob in the legally required manner is called "service of process."
The hard part is not filing the lawsuit, but serving Bob with process. But, if you have his name there is a simplified private investigator service called a "skip-trace" that you can pay someone to do in order to locate someone when you have their name and any other details that you can provide about them. This can be as cheap as $50 with payment due only if the investigator is successful, and as expensive as a couple of thousand U.S. dollars if it is a particularly challenging case that is due whether or not the investigator is successful.
In my experience, if you have the correct name for a person and know enough to distinguish which of several people with the same name of different ages and addresses is the person you are looking for, a skip-trace can typically locate that person about 90% of the time. If you know which city the person is in and their approximate age, your odds of success are even higher, unless the person has a very common name indeed (e.g., John Smith, or Jose Garcia, or Tom Nguyen).
A full service private investigator with a sufficiently large budget can go beyond a skip-trace to try sneaky ways to locate Bob's address when it is extremely hard to find (for example, duping a receptionist at an exchange to reveal information under the pretense of being a friend who wants to send him a gift, or talking to someone who works at the exchange about it after buying them drinks at a bar the P.I. figures out that they frequent, or decoding an internal reference code and using that to figure out additional information about Bob that facilitates finding his address, or entering into to fake deal with Bob in getting his contact information in the process of doing so) and has maybe a 25%-75% chance of success depending on how clever and skilled the P.I. is at their job. If the dollar amount of the dispute is large enough (perhaps hundred of thousands of dollars) and is likely to be collectible if the lawsuit is successful, this money may be worth it.
Once you have the name and a location, you then hire a process server to deliver a summons, a complaint (the legal document initiating the lawsuit) and sometimes other documents such as exhibits to the complaint and form cover sheets and/or required disclosures to those documents. Process services are very good at their jobs and usually get the papers delivered, but, of course, they don't have a 100% success rate either.
Once a process server delivers these papers to Bob, he has to respond by a certain deadline established by court rules. If he does not, the court enters a default judgment against Bob for the full amount of relief requested in the complaint, sometimes together with a damages hearing.
Once Bob either files papers responding to the complaint, or defaults, you can then issue a subpoena to third-parties with regard to any information relevant to the lawsuit that is not admitted by Bob, for use at trial or in a damages hearing on a default judgment.
But in most cases, both at the federal level and in most U.S. state courts, it is not possible to issue a subpoena to someone until a lawsuit has been filed and the person sued has been served with process and either answered or defaulted. So, generally, you can't use a subpoena to get contact information about the person you are suing (unless you are, for example, a grand jury, or a prosecutor, or a Congressional committee, or a government law enforcement or regulatory official with subpoena power).
A minority of U.S. states, however, are exceptions to this rule and allow subpoenas to be issues for very limited information, such as contact information for a potential party or disclosure of a small number of key documents, before a lawsuit is filed. The same is true of non-U.S. common law jurisdictions. Some allow very limited pre-lawsuit discovery and some don't.
Arguably, you might be able to ask a court to allow you to deliver the papers commencing the lawsuit against Bob by appointing the exchange or intermediary as his agent for the limited purpose of delivering legal papers to him that would be considered binding upon him, if you were not able to locate Bob's address with reasonable diligence (such as hiring a private investigator to do a skip-trace) which is called "substituted service" and has to be fashioned on a case by case basis in a manner consistent with constitutional due process considerations. Whether a court would allow substituted service upon Bob in these circumstances would be a close call legally.
There are also certain kinds of lawsuits, called "in rem" actions, in which you don't need to personally deliver documents to Bob and it is sufficient to put him on notice of the lawsuit by publication instead. Actions "in rem" include actions actions to determine who owns property, actions to take possession of property, probate cases, civil forfeiture cases, and actions seeking to dissolve a marriage (without a binding resolution of alimony and child support issues). But the kind of lawsuit described in the question would be an "in personam" action rather than an "in rem" action which is only possible with delivery of the documents to Bob or to someone with a close connection to him who could be trusted to pass the papers onto him.
Obviously, the better course of action for people in Alice's position is to refuse to enter into contract negotiations until you have the other party's full name and contact information. But people like Alice often learn that lesson in the school of hard knocks, as it is rarely something that they teach you, for example, in business school.
If you are dealing with a legally organized business entity, Bob Co, Inc., that actually exists (or if Bob is doing business under a legally filed trade name) instead of just doing business with Bob Smith, the person, you are in a much better situation. This is because legally organized business entities and people doing business under trade names are required by law to make contact information a matter of public record. You may have to hire a private investigator to search public records in all 50 states to find that contact information, but the odds of ultimate success in that case are on the order of 98% and once that information is available a process server has basically a 99.5% chance of quickly and easily meeting the legal requirement to deliver the papers to that company.
Once Bob responds to the lawsuit, you can get additional information from Bob and/or third-parties in what is called "discovery" to support your lawsuit thought a mandatory court process and you can amend your initial complaint to reflect the information that you have newly discovered if you do so in a timely fashion.
