It is not required but recommended. U.S. citizens who change their names may travel using a U.S. passport that was issued in their prior name, but need proof of the name progression, according to U.S. Customs and Border Protection (e.g. marriage certificate, divorce decree or court documents showing the legal name change).
It is recommended that travelers check with the countries they are traveling to for their entry requirements.
U.S. CBP also recommends calling the Transportation Security Administration to find out their latest requirements about name matching on travel documents.
For more seamless travel, it's a good idea to change the name on your passport.