Yes, September 11th is officially designated as Patriot Day in the United States. It is a national day of observance and remembrance for the 2,977 people killed in the terrorist attacks of September 11, 2001. The day serves to honor the victims, their families, and the first responders who sacrificed their lives.
The designation was established shortly after the attacks. On December 18, 2001, President George W. Bush signed into law Public Law 107-89, a joint resolution of the U.S. Congress that designated September 11th of each year as "Patriot Day." In 2009, Congress and President Barack Obama further designated the date as a "National Day of Service and Remembrance," encouraging Americans to engage in charitable service and community activities as a tribute.
By law, the President directs that the flag of the United States be flown at half-staff at all U.S. government buildings and establishments, both at home and abroad. The President also asks Americans to observe a moment of silence beginning at 8:46 a.m. (Eastern Daylight Time), the time the first plane struck the North Tower of the World Trade Center. This day is a solemn commemoration rather than a federal holiday, meaning most businesses and schools remain open.