Go to the website of the county court where you suspect the person changed her name. Some counties offer searchable online records of the cases they have on file. Search for any name change petitions in the person's former name. You can also search for divorce records, because a maiden name can be restored in a divorce.
Go to the Clerk of the Court's office in the appropriate county, if there is not an online database. Some counties have public computer terminals you can use to look up information on filed cases. If you see a name change or divorce case for the person, ask the court to get the court file for you. Read through the file to determine if the court granted a change of name. If the county does not have a public computer terminal, ask the clerk to conduct a records search for you. You will probably have to pay a fee for the service.
Contact the Department of Vital Statistics or Records in the state to see what information it has publicly available. The state may give you a copy of a divorce decree or birth certificate under some circumstances. If the person changed her name in the divorce or changed her birth certificate, you might find the information you want. Many states do not give this information out to the public for privacy reasons.
Employ an online service or private investigator to search public records for the information. For a fee, some services will search all publicly available information in the United States for the records. A private investigator might travel to multiple courthouses in the areas where the person has lived, in order to check the records.