Probably not until and unless the process server gets the correct address and actually serves you. Then the documents should explain the matter fully.

If the person who was attempted to be served took note of the court involved, and told you what court it was, you could call the Clerk of the Court and inquire.

Otherwise you would need to ask every possible court, which would take a great deal of time and effort.

You have not been lawfully served (at least not in most US jurisdictions) until you have been served in person, or perhaps by mail, or by publication in a newspaper, or in some other way considered lawful in your jurisdiction, but serving a person at your old address is not likely to be valid service. (Valid methods differ from one jurisdiction to another, and in some situations differ by the kind of case involved.) If the person at your old address gave the server your new address, s/he will probably be along shortly.

If a process server is given an address by the client (plaintiff), s/he may well go there first, and only do research later in case the first address is wrong. One need not worry about it until the papers are served, but it might be wise to read the legal ads in any nearby large newspapers for a few weeks, in case of service by publication. The papers should give the name of a court, and perhaps the name of a judge. You can call the clerk of the court and find out if the papers are legit. There may well be a docket no or case no or some other identifying umber, as well. This will help in verification. Docketed cases may be listed on a court web site.